**Depression and Serotonergic Changes during the Climacteric and Postmenopausal Stages: Hormonal Influences**

Rosa Isela García-Ríos, Armando Mora-Pérez and Cesar Soria-Fregozo

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.69786

### **Abstract**

Depression is a psychiatric disorder that affects a high percentage of women. Most of the depression disorders turn up during the premenopause and perimenopause stages when the hormonal oscillations make an impact in the brain function principally on the serotonergic system, which is related to neurobiology of depression. 5-HT1A and 5-HT2A receptors change on functionality and density in afferent areas related to emotional modulation and increased serotonin clearance, and the binding potential of serotonin transport has been related to the underlying mechanism of the depression during the climacteric or postmenopausal stage. Some findings have been proven on preclinical studies. These studies on animals have recognized how estrogen treatment activates intracellular signaling pathways as mitogen-activated protein (MAP)/extracellular signal-regulated kinase (ERK), tyrosine kinase brain-derived neurotrophic factor receptor (TrKB), insulin-like growth factor-1 receptor (IGF-1R), phosphatidylinositol 3-kinase (PI3)/serine/threonine-specific protein kinase (Akt), and metabotropic glutamate receptor 1 (mGluR1) which interact with the serotonergic system to allow establishment of the estradiol effects on mood regulation. Thus, the interaction between the woman's reproductive status and the serotonin changes could be useful to create prevention strategies, early diagnosis, and medical treatment of climacteric and postmenopausal women with depression, in order to improve their quality of life.

**Keywords:** depression, menopause, climacteric, 5-HT1A receptor, 5-HT2A receptor, estradiol

© 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

### **1. Introduction**

Depression is one of the most common psychiatric disorders that affect approximately 4.84% people around the world, and it is considered to be one of the principal causes of disability worldwide [1]. According to the Global Burden of Disease study report in 2015 [2], the highest rates of disability-adjusted life years (DALYs) worldwide are established on women aged 15–49 years with 5.65%, followed by 50–69 years old women with 2.98% and 70 years old with 1.26%. DALYs represent the years of life that are adjusted by a certain level of disability experienced during a particular period of time, related to depressive disease. It supports studies which demonstrate that most of the depression disorder comes out during the premenopause and perimenopause stages.

During the beginning of menopausal stage or in the postmenopausal stage, women are more susceptible to suffer depression disorder with more severe and longer symptoms [3, 4]; severity of depression has been related to the ovarian hormone oscillating levels in the premenopause and very low levels in early postmenopause, specifically with estrogens [5].

The climacterium stage is a period of time that includes the perimenopause, premenopause, and menopause (see **Figure 1**); in this stage the women estrogenic oscillating, produces a dysfunction on the serotonergic neurotransmission system which is related to the high prevalence of depression in such stages compared with women in postmenopausal stage. However, this relationship seems to be controversial because not all the studies reported an increased prevalence of depression in the climacteric stage, when women's groups from different ethnic cultures, ages, school grade, and civil status, among others, were evaluated. These divergences on the clinical study results could be partially justified by different neurochemical changes related to the effects of estradiol on serotonergic system and the influence of these changes on the establishment of depression during the different stages of the climacteric period. For example, on early premenopausal stage, there is a decrease on the 5-HT1A autoreceptors in raphe, which is a brain structure responsible for the serotonin (5-HT) synthesis, and an increase on the 5-HT1A postsynaptic receptors located on the hippocampus (both receptors enable the antidepressant clinically effective, as the selective inhibitors of the serotonin, e.g., the fluoxetine) related to the high hormonal concentration compared with postmenopausal women [6].

**Figure 1.** Classification of the reproductive phases of the woman. This classification is an abstract of the reproductive stage of women with their approximate during. Ovaries function markers and hormonal levels can help to make a correct classification. Modified from [57].

Thus, this can be related with the different antidepressant responses along the climacteric and postmenopausal stages.

**1. Introduction**

64 A Multidisciplinary Look at Menopause

and perimenopause stages.

correct classification. Modified from [57].

Depression is one of the most common psychiatric disorders that affect approximately 4.84% people around the world, and it is considered to be one of the principal causes of disability worldwide [1]. According to the Global Burden of Disease study report in 2015 [2], the highest rates of disability-adjusted life years (DALYs) worldwide are established on women aged 15–49 years with 5.65%, followed by 50–69 years old women with 2.98% and 70 years old with 1.26%. DALYs represent the years of life that are adjusted by a certain level of disability experienced during a particular period of time, related to depressive disease. It supports studies which demonstrate that most of the depression disorder comes out during the premenopause

During the beginning of menopausal stage or in the postmenopausal stage, women are more susceptible to suffer depression disorder with more severe and longer symptoms [3, 4]; severity of depression has been related to the ovarian hormone oscillating levels in the premeno-

The climacterium stage is a period of time that includes the perimenopause, premenopause, and menopause (see **Figure 1**); in this stage the women estrogenic oscillating, produces a dysfunction on the serotonergic neurotransmission system which is related to the high prevalence of depression in such stages compared with women in postmenopausal stage. However, this relationship seems to be controversial because not all the studies reported an increased prevalence of depression in the climacteric stage, when women's groups from different ethnic cultures, ages, school grade, and civil status, among others, were evaluated. These divergences on the clinical study results could be partially justified by different neurochemical changes related to the effects of estradiol on serotonergic system and the influence of these changes on the establishment of depression during the different stages of the climacteric period. For example, on early premenopausal stage, there is a decrease on the 5-HT1A autoreceptors in raphe, which is a brain structure responsible for the serotonin (5-HT) synthesis, and an increase on the 5-HT1A postsynaptic receptors located on the hippocampus (both receptors enable the antidepressant clinically effective, as the selective inhibitors of the serotonin, e.g., the fluoxetine) related to the high hormonal concentration compared with postmenopausal women [6].

**Figure 1.** Classification of the reproductive phases of the woman. This classification is an abstract of the reproductive stage of women with their approximate during. Ovaries function markers and hormonal levels can help to make a

pause and very low levels in early postmenopause, specifically with estrogens [5].

The 5-HT2A receptors located on brain areas such as prefrontal cortex contribute on regulating the release of the 5-HT to areas that modulate the amygdala reactivity, brain structure involved to the emotional regulation. Treatment with 17β-estradiol for postmenopausal women increases the 5-HT2A receptors in prefrontal cortex [7]. However, the possible association between the establishment of depression in different climacteric and postmenopausal stages with the 5-HT2A receptor's activity has not been explored. Nevertheless, the preclinical data support the involvement of these receptors on the regulation of the depression disorder [8, 9].

On the other hand, in healthy postmenopausal women, there is a relation between personality features such as extroversion, aggressiveness, and neuroticism with the serotonin transporter (5-HTT). 5-HTT promotes polymorphism with "s" allele, which implies 5-HTT low expression and an increase in the impulsivity. Likewise, this trait is related with monoamine oxidase A (MAO-A) polymorphism that produces an increase of climacteric and depressive symptoms [10, 11]. In contrast, women under 50 years old with the "l" allele 5-HTT present a better antidepressant response and neural protection against the suicide attempt [12]; however, this response disappears when there is a low hormonal activity during menopausal stage [13].

Therefore, the main objective of this work is to collect and review scientific data not only clinical but also preclinical data that allow us to explain the knowledge about the impact of hormonal change experienced during climacteric and postmenopausal stages and how it affects serotonin neurotransmission that may contribute to the establishment of the depression disorder and the therapeutic response to antidepressant drugs.

### **2. Influence of hormones on the depression disorder establishment**

Some researches point out a high vulnerability to suffer depression disorder on the women reproductive stage, related to the hormonal changes, as a decrease on the estradiol levels and an increase on the follicle-stimulating hormone (FSH) levels on the perimenopausal [3, 14, 15] throughout different reproductive stages it is set basically two different aspects about the hormonal influences, principally estradiol with the increasing risk to set out depressive symptomatology. The first one establishes that low hormonal concentrations on estradiol and progesterone during the earlier follicular stage of the menstrual cycle of the earlier productive stage of a woman are related to premenstrual dysphoric syndrome characterized among some other symptoms by depression and anxiety [16]. The second one suggests that oscillations on the hormonal levels on early stages of the menopause transition are determinant to increase the risk of having some depressive incidences. The same effect is observed on women who had been throughout menopause by surgical procedure, thus, became on the decrease of the hormonal levels, and also there is a surgical post-period where they show hormonal oscillations because the renal glands try to supply the hormonal lost, but it is important to mention that women who had been in a surgical procedure, such as oophorectomy on early age, indicate an increased probability to depression disease with severe and longer symptoms compared to women with a natural menopause [17].

There is a relationship at the establishment on depressive symptomatology with FSH or high luteinizing hormone (LH) levels and low inhibin B levels; this is a glycoprotein hormone secreted by teak and granulosa cells from the pre-antral and antral follicles that was responsible for the inhibition of FSH production at the level of the pituitary gland and a huge variability on estradiol levels, which occur during the menopause transition that includes women on the premenopause and perimenopause [2, 3]. Likewise, there is a FSH levels increasing and an abrupt fall of the estrogen levels after 12 months of menopause considered as early postmenopausal [18] pattern, which is independently from the sample analyzed on the late premenopausal and postmenopausal stage. Those hormonal variations are related to a rise on depression prevalence for 10 years before and 8 years after the last menstrual cycle and fall on the late postmenopausal period [4]. The above suggests that alterations in the feedback of the hypothalamic-pituitary-gonadal axis consequence of changes on the concentrations of ovarian hormone through the climacteric and postmenopausal stages, carry out a fundamental place on women's emotional stability, through the regulation of brain plasticity and neurochemical changes.

It has been established an association between a delay in appearance of menopause transition, in a period of two more years than average with 2% of decrease on the risk of a depression disease during the postmenopause, and also a reduction of the 50% to suffer depression disease on women who have menopause after 40 years old compared with early menopause on women before that age. It is suggested that those findings could be attributed to longer exposure to the endogenous estrogens that develop a neural protection and antidepressive effect [19]. This effect seems to be associated with the cerebral changes that induce the hormonal diminution according to the age of the woman.

The antidepressant effect on hormone replacement therapy (HRT) or estrogenic therapy on menopausal women is controversial. The estrogen supply such as 17β-estradiol (100 μg/day) has a lack of antidepressant effects on depressed women during the postmenopausal period on the late stage; it is to say that, 17 years after the menopausal stage, they show a FSH (≥40 pg/ml) and estradiol (≤19.7 pg/ml) hormonal concentrations [20]. This lack of antidepressant effect is also observed in postmenopausal women in the early phase, approximately 6 months to 3 years after menopause, with hormonal concentrations of FSH ≥ 35 pg/ml and estradiol ≤ 40 pg/ml, when 50 μg/day or 84 μg/day of estradiol was administered [7, 21]. The loss of estrogen efficacy against depression in women with postmenopausal may be associated with the downregulation of αand β-estrogenic receptors at the brain level, caused by continued decrease of plasma estradiol concentrations. In contrast, antidepressant effects have also been reported in postmenopausal women with replacement treatments with bioidentical hormones (80% estriol/20% estradiol; 0.25 to 0.5 mg) and/or progesterone (20 to 60 mg), by transdermal injection in a volume of 1 ml/day for a period of 8 weeks. These women present an improvement in the depressive and anxiety symptoms according to Hamilton scales, at 2 months of treatment and annually until 36 months. Treatment with bioidentical hormones improved the health and quality of life of women without reports of adverse side effects. However, these women cursed postmenopausal, after an oophorectomy with a mean age of 52.3 ± 9.6 years and the time that elapsed since the surgery was not described, so it cannot be specified whether it was in the early or late stage of postmenopause [22]. This suggests that the type of molecule used for hormone replacement therapy and probably the age at which it is given could determine therapeutic success, a possibility that remains to be explored.

lost, but it is important to mention that women who had been in a surgical procedure, such as oophorectomy on early age, indicate an increased probability to depression disease with

There is a relationship at the establishment on depressive symptomatology with FSH or high luteinizing hormone (LH) levels and low inhibin B levels; this is a glycoprotein hormone secreted by teak and granulosa cells from the pre-antral and antral follicles that was responsible for the inhibition of FSH production at the level of the pituitary gland and a huge variability on estradiol levels, which occur during the menopause transition that includes women on the premenopause and perimenopause [2, 3]. Likewise, there is a FSH levels increasing and an abrupt fall of the estrogen levels after 12 months of menopause considered as early postmenopausal [18] pattern, which is independently from the sample analyzed on the late premenopausal and postmenopausal stage. Those hormonal variations are related to a rise on depression prevalence for 10 years before and 8 years after the last menstrual cycle and fall on the late postmenopausal period [4]. The above suggests that alterations in the feedback of the hypothalamic-pituitary-gonadal axis consequence of changes on the concentrations of ovarian hormone through the climacteric and postmenopausal stages, carry out a fundamental place on women's emotional stability, through the regulation of brain plasticity and neuro-

It has been established an association between a delay in appearance of menopause transition, in a period of two more years than average with 2% of decrease on the risk of a depression disease during the postmenopause, and also a reduction of the 50% to suffer depression disease on women who have menopause after 40 years old compared with early menopause on women before that age. It is suggested that those findings could be attributed to longer exposure to the endogenous estrogens that develop a neural protection and antidepressive effect [19]. This effect seems to be associated with the cerebral changes that induce the hormonal

The antidepressant effect on hormone replacement therapy (HRT) or estrogenic therapy on menopausal women is controversial. The estrogen supply such as 17β-estradiol (100 μg/day) has a lack of antidepressant effects on depressed women during the postmenopausal period on the late stage; it is to say that, 17 years after the menopausal stage, they show a FSH (≥40 pg/ml) and estradiol (≤19.7 pg/ml) hormonal concentrations [20]. This lack of antidepressant effect is also observed in postmenopausal women in the early phase, approximately 6 months to 3 years after menopause, with hormonal concentrations of FSH ≥ 35 pg/ml and estradiol ≤ 40 pg/ml, when 50 μg/day or 84 μg/day of estradiol was administered [7, 21]. The loss of estrogen efficacy against depression in women with postmenopausal may be associated with the downregulation of αand β-estrogenic receptors at the brain level, caused by continued decrease of plasma estradiol concentrations. In contrast, antidepressant effects have also been reported in postmenopausal women with replacement treatments with bioidentical hormones (80% estriol/20% estradiol; 0.25 to 0.5 mg) and/or progesterone (20 to 60 mg), by transdermal injection in a volume of 1 ml/day for a period of 8 weeks. These women present an improvement in the depressive and anxiety symptoms according to Hamilton scales, at 2 months of treatment and annually until 36 months. Treatment with bioidentical hormones improved the health and quality of life of

severe and longer symptoms compared to women with a natural menopause [17].

chemical changes.

66 A Multidisciplinary Look at Menopause

diminution according to the age of the woman.

Changes in plasma levels of FSH on the establishment of depression in women with natural menopause are also seen in women with oophorectomy [23]; since the ovaries are removed, there is an abrupt cessation in the production of testosterone that is aromatized to estrogen and estradiol, which results in a dysfunction in the hypothalamic-pituitary-gonadal axis increasing FSH and LH levels, with the consequent decline of estradiol and progesterone levels [24]. These changes in hormone levels undergoing surgery take from 2 to 3 months to stabilize and are associated with a decrease in depressive symptoms [23]. Women undergoing menopause induced by surgeries such as hysterectomy and/or oophorectomy increase up to four times the probability to suffer postsurgery depression [25]. However, women who have undergone some depressive episode prior to surgery report a decrease in postoperative depressive symptomatology [25]. This may reflect a paradoxical effect. Some of the answers might be in the interrelation between estrogen and the serotonergic system.

### **3. Serotonergic alterations during the climacteric and postmenopause related with depression**

A study by Stein et al. [6] detected an increase on 5-HT1A receptor levels in the hippocampus and a decrease in the dorsal nucleus raphe of premenopausal women at early ages (24.1 ± 2.6 years) compared to postmenopausal women (55.2 ± 4.8 years). In this same study, they identified higher concentrations of progesterone, estradiol, dehydroepiandrosterone sulfate (DHEAS), and cortisol in premenopausal women compared to postmenopausal women. This suggests that these hormones could be involved in the regulation of the expression of 5-HT1A receptors in different brain areas in women who travel through the climacteric, intervening in the establishment of depressive disorders of this stage, as well as in the different therapeutic responses to antidepressant drugs, and probably contributing to the effect of drug resistance, depending on the levels of receptors affected by oscillations on concentrations of hormones, mainly produced by the ovaries.

Studies made with positron emission tomography with [carbonyl-C11] WAY-100635 show that in the dorsal nucleus raphe, a structure highly involved in the regulation of serotonergic neurotransmission and therefore with a high density of 5-HT1A receptors, there is 1.5 times more 5-HT1A receptors in the luteal phase than in the follicular phase in healthy women, whereas this proportion is not observed in women with premenstrual dysphoric disorder [26], so a dysfunction like this could be a factor underlying to the establishment of depressive symptoms. Although Drevets et al. [27] reported a reduction in 5-HT1A receptors in the raphe (41.5%) and neocortical and limbic areas (25–33%) in depressed patients [27]. In this study the sex of the patients was not discriminated, and only from 4 to 7% of the patients were women and do not described the age neither conditions of the reproductive phase, so these results should be taken with reservation.

Moses-Kolko et al. [28] reported that in depressed women going through premenopause and postmenopause, there is a 15% decrease in 5-HT1A receptors in the orbitofrontal cortex compared to adult men with depression. The foregoing after performing an endocrine standardization to minimize the influence introduced by endogenous hormonal fluctuations and reproductive stage. They also detected an increase in the potential binding to 5-HT1A receptors in women, as age increases. They estimate that there is a 4.5% reduction per decade of age in the number of 5-HT1A receptors in the raphe in women. The 5-HT1A receptors have an age-dependent increase in neocortical regions in women, associated with decreased estrogen. In the same study, they identified that increase in 5-HT2A receptors is associated with the establishment of disorders such as neurosis, depression, suicide, and eating disorders [28], suggesting that age tends to reduce these receptors, since they are expressed in the neuropil of pyramidal neurons located mainly in the neocortex which are related to the release of glutamate and gamma-aminobutyric acid (GABA) regulating the postsynaptic excitatory impulses that project to the hippocampus and spinal cord neurons [29]. So, it is hypothesized that its reduction associated with age may be related to sleep disorder, cognition, and mood disorders [30].

### **4. Serotonergic changes associated to antidepressants and hormone replacement in the climacteric and postmenopause**

The HRT in women undergoing climacteric, with 17β-estradiol by means of transdermal patches at a mean dose of 93 μg/day, causes an increase in plasma levels of estradiol from 14.7 pg/ml at baseline versus 176.5 pg/ml, after 10.2 weeks of treatment. This increase in estrogen levels has been related to the establishment of antidepressant effects after HRT [7]. However, several studies suggest that estrogens have the capability to produce a modulating effect on the serotonergic system that contributes to the establishment of the antidepressant effect (see **Table 1**).

In surgically postmenopausal women (58.4 age and 7.5 years after oophorectomy) and, therefore, with very low plasmatic concentrations of estradiol, the treatment with estradiol reduces the potential binding of 5-HTT in brain structures, such as in the amygdala, in the frontal cortex, and in various cortical regions. While the treatment with estradiol and testosterone reduces it in the parahippocampal gyrus, insular cortex, caudate nucleus, and thalamus [31]. Hence, the hormonal treatment reduces the efficiency of 5-HTT and increases the availability of 5-HT in the synaptic cleft on structures involved in the emotion modulation. This fact could be associated to an improvement in depressive symptomatology of these women measured with Beck Depression Inventory test [31]. However, some studies indicate that estrogen therapy in postmenopausal women does not produce antidepressant effects [21, 24], probably due to the downregulation of estrogenic receptors, associated with chronic decrease of

### *Changes associated to condition without pharmacological treatment*

sex of the patients was not discriminated, and only from 4 to 7% of the patients were women and do not described the age neither conditions of the reproductive phase, so these results

Moses-Kolko et al. [28] reported that in depressed women going through premenopause and postmenopause, there is a 15% decrease in 5-HT1A receptors in the orbitofrontal cortex compared to adult men with depression. The foregoing after performing an endocrine standardization to minimize the influence introduced by endogenous hormonal fluctuations and reproductive stage. They also detected an increase in the potential binding to 5-HT1A receptors in women, as age increases. They estimate that there is a 4.5% reduction per decade of age in the number of 5-HT1A receptors in the raphe in women. The 5-HT1A receptors have an age-dependent increase in neocortical regions in women, associated with decreased estrogen. In the same study, they identified that increase in 5-HT2A receptors is associated with the establishment of disorders such as neurosis, depression, suicide, and eating disorders [28], suggesting that age tends to reduce these receptors, since they are expressed in the neuropil of pyramidal neurons located mainly in the neocortex which are related to the release of glutamate and gamma-aminobutyric acid (GABA) regulating the postsynaptic excitatory impulses that project to the hippocampus and spinal cord neurons [29]. So, it is hypothesized that its reduction associated with age may be related to sleep disorder, cognition, and mood

**4. Serotonergic changes associated to antidepressants and hormone**

The HRT in women undergoing climacteric, with 17β-estradiol by means of transdermal patches at a mean dose of 93 μg/day, causes an increase in plasma levels of estradiol from 14.7 pg/ml at baseline versus 176.5 pg/ml, after 10.2 weeks of treatment. This increase in estrogen levels has been related to the establishment of antidepressant effects after HRT [7]. However, several studies suggest that estrogens have the capability to produce a modulating effect on the serotonergic system that contributes to the establishment of the antidepressant effect (see

In surgically postmenopausal women (58.4 age and 7.5 years after oophorectomy) and, therefore, with very low plasmatic concentrations of estradiol, the treatment with estradiol reduces the potential binding of 5-HTT in brain structures, such as in the amygdala, in the frontal cortex, and in various cortical regions. While the treatment with estradiol and testosterone reduces it in the parahippocampal gyrus, insular cortex, caudate nucleus, and thalamus [31]. Hence, the hormonal treatment reduces the efficiency of 5-HTT and increases the availability of 5-HT in the synaptic cleft on structures involved in the emotion modulation. This fact could be associated to an improvement in depressive symptomatology of these women measured with Beck Depression Inventory test [31]. However, some studies indicate that estrogen therapy in postmenopausal women does not produce antidepressant effects [21, 24], probably due to the downregulation of estrogenic receptors, associated with chronic decrease of

**replacement in the climacteric and postmenopause**

should be taken with reservation.

68 A Multidisciplinary Look at Menopause

disorders [30].

**Table 1**).

*Changes associated to condition and estrogen replacement therapy*

*Changes associated to condition and estrogen replacement therapy*

5-HTT, serotonin transporter; 5-HT, 5-hidroxytriptamine; ↑, increase; ↓, decrease; SSRI, selective serotonin reuptake inhibitors

**Table 1.** Clinical and preclinical studies of the relation between serotonergic system and hormones.

concentrations of estradiol in the postmenopausal stage. This hypothesis is based on the fact that estrogenic antidepressant treatment on perimenopausal women produces therapeutic effects [32], probably because they still have considerable concentrations of estradiol, compared to postmenopausal women, which contribute that they do not present important neurochemical changes on estrogen receptors. In support, depressed postmenopausal women treated simultaneously with the combination of antidepressant serotonin-specific reuptake inhibitor drugs, such as fluoxetine with estrogen, showed significantly greater improvement of both mood and quality of life compared to fluoxetine monotherapy [33]. Pointing out that estrogen by itself probably does not produce antidepressant effects, the reduction that exerts on the potential binding of 5-HTT is enough to increase synaptic 5-HT concentration, a synergistic effect on serotonergic system of both estrogen and fluoxetine, which contributes to the establishment of the antidepressant effect. Paradoxically, the combination with tibolone, a synthetic steroid, does not produce synergistic antidepressant effects with fluoxetine [34]. The above suggests that substituents on steroid molecules could be a determinant in the potential interrelation in therapeutic efficacy between steroids and the serotonergic system.

On the other hand, some studies observed an increase on hypersensibility of postsynaptic 5-HT2A receptors on the basis of neurobiological depression [35, 36]. The 5-HT2A receptor is related to regulating the 5-HT release on the protection of neurons which are located on the prefrontal cortex, thus, to help the regulation easier to the amygdala's reaction and some other behaviors related. The administration of 150 mg/day of clomipramine for 3 weeks, tricyclic antidepressant, results a descend of 5-HT2A receptor's occupation on neocortex area, calculated by positron emission tomography (PET) which coincide with depression scores significantly improved, denoting the probability of the clomipramine's interaction with those receptors or may cause modified signal mechanism of these receptors [37].

There is a relationship with ovarian hormone and the 5-HT2A receptors. Kugaya et al. [7] developed a study on postmenopausal women, classified by the concentrations of FSH ≥30 UI/L. Those women were treated with 17β-estradiol HRT for almost 3 months; by PET that 5-HT2A serotonin receptors increased principally on brain areas such as prefrontal cortex and anterior cingulate cortex, related to increase of plasmatic estradiol density, this study did not mark any changes related to the effects on the mood but could be the result related to the test characteristics and the few subjects of study [7].

### **5. Preclinical studies of serotonergic changes associated with hormones and ovariectomy**

concentrations of estradiol in the postmenopausal stage. This hypothesis is based on the fact that estrogenic antidepressant treatment on perimenopausal women produces therapeutic effects [32], probably because they still have considerable concentrations of estradiol, compared to postmenopausal women, which contribute that they do not present important neurochemical changes on estrogen receptors. In support, depressed postmenopausal women treated simultaneously with the combination of antidepressant serotonin-specific reuptake inhibitor drugs, such as fluoxetine with estrogen, showed significantly greater improvement of both mood and quality of life compared to fluoxetine monotherapy [33]. Pointing out that estrogen by itself probably does not produce antidepressant effects, the reduction that exerts on the potential binding of 5-HTT is enough to increase synaptic 5-HT concentration, a synergistic effect on serotonergic system of both estrogen and fluoxetine, which contributes to the establishment of the antidepressant effect. Paradoxically, the combination with tibolone, a synthetic steroid, does not produce synergistic antidepressant effects with fluoxetine [34]. The above suggests that substituents on steroid molecules could be a determinant in the potential interrelation in therapeutic efficacy between steroids and the serotonergic system. On the other hand, some studies observed an increase on hypersensibility of postsynaptic 5-HT2A receptors on the basis of neurobiological depression [35, 36]. The 5-HT2A receptor is related to regulating the 5-HT release on the protection of neurons which are located on the prefrontal cortex, thus, to help the regulation easier to the amygdala's reaction and some other behaviors related. The administration of 150 mg/day of clomipramine for 3 weeks, tricyclic antidepressant, results a descend of 5-HT2A receptor's occupation on neocortex area,

5-HTT, serotonin transporter; 5-HT, 5-hidroxytriptamine; ↑, increase; ↓, decrease; SSRI, selective serotonin reuptake

Inhibits the 5-HTT Estradiol (20 pmol) in the CA3

Slowing of the 5-HT clearances, as well as an inhibition of the ability of fluvoxamine (SSRI antidepressant) to slow the clearance of 5-HT

**Condition (average age) Serotonergic system changes Regimen of treatment and/or**

Canceled the antidepressive-like effect of fluvoxamine (10 mg/kg)

**Table 1.** Clinical and preclinical studies of the relation between serotonergic system and hormones.

in forced swim test

*Changes associated to condition and estrogen replacement therapy*

Acute administration of both 17β-estradiol in the CA3 region of the hippocampus and systemic administration of estradiol benzoate (25 μg/100 μl, s.c., 48 hours before progesterone) + progesterone (500 μg/100 μl, s.c., 24 hours before the test)

**changes associated to treatment**

Estradiol benzoate (25 μg/100 μl, s.c., 74–75 hours before the test and 24 hours before progesterone) + progesterone (500 μg/100 μl, s.c., 24 or 74–75 hours before the test)

region of the hippocampus but not in 10 months in females, even at

<40 pmol doses

[41]

**References**

[42]

[51]

Female rats (1–2 months)

70 A Multidisciplinary Look at Menopause

Female rats (2–3 months) 2–3 weeks postovariectomy

Female rats (4 months) Two weeks of postovariectomy

inhibitors

2–3 weeks of postovariectomy

> Studies made in rodents have also shown the interrelation between estrogen and serotonergic system. Coadministration of estradiol with fluoxetine has been shown to contribute to 5-HT1A receptor desensitization [38], which is associated with antidepressant effect in humans and in rats evaluated in behavioral despair models [38]. In addition, this combination of estradiol with fluoxetine inhibits 5-HTT and increases de novo brain serotonin synthesis by activating tryptophan hydroxylase enzyme [39]. At the same time, it increases the number and sensitivity of the 5-HT1A receptors, mainly in the dorsal nucleus raphe of rats. This could be related to the antidepressant effect produced by estradiol.

> It has also been detected that acute administration of estradiol on ovariectomized rats increased the turnover of serotonin, by increasing serotonin and its metabolite, 5-hydroxyindoleacetic acid (5-HIAA) in amygdale and striatum involved in the mood regulation. While chronic for 16 days, estradiol and progesterone administration has been found to increase serotonin mainly in the dorsal raphe of the ovariectomized rats [40].

> Benmansour and collaborators' research group [41] has explored the signaling mechanisms involved in the interaction of estradiol and serotonergic systems in rats. Both acute administration of 17β-estradiol in the CA3 region of the hippocampus and systemic administration of estradiol benzoate cause slowing of the 5-HT clearances, as well as an inhibition of the ability of fluvoxamine to slow the clearance of 5-HT [41]. These effects are mediated by estrogen receptors α and β. The slowing of the 5-HT clearance was due to activation of β-estrogen and/or GPR30. Meanwhile, the blockade of fluvoxamine's inhibitory effect on 5-HT clearance was mediated by α-estrogen [42]. Both of them used different signaling mechanisms. The estradiol-induced slowing of serotonin clearance by means of activation of receptors of β-estrogen required MAPK/ ERK1/2 signaling pathways and involved interactions both with tyrosine kinase BDNF receptor (TrKB) and insulin-like growth factor-1 receptor (IGF-1R). The effect of estradiol to prevention of the ability of fluvoxamine to slow serotonin clearance, through receptors of α-estrogen, required MAPK/ERK1/2 and PI3K/Akt signaling pathways as well as interactions with both IGF-1R and mGluR1 [43]. All these ways are etiologically implied to depression.

In this context, the ERK signaling cascade is activated by antidepressant clinically effective as fluoxetine [44] and the systemic blockade of the MAPK pathway in mice produced depressive-like behavior in several animal models of experimental depression as well as inhibits the antidepressant effect of desipramine and fluoxetine in the forced swim test, a main model of depression [45]. On the other hand, the action of BDNF, which has been implicated in the mechanism(s) of action of the antidepressant (see Ref. [46]), is mediated through its high-affinity tyrosine kinase receptor B (TrkB), whose activation is required for antidepressant-like effect [47].

The acute intraventricular administration of IGF-1 produced antidepressant-like effects in mice evaluated in the tail suspension and forced swim tests [48], an effect detected after 3 days of the administration with participation of 5-HT [49]. The antagonism of the mGluR produced antidepressant-like effects in the forced swim test, probably through the intracellular signaling pathways described above [50]. Therefore, there is evidence about the interaction with the estrogens and the serotonergic system on the regulation on the depression disorder not only removing them but also influencing them by the other neurotransmitter systems and other kinds of receptors.

We have already mentioned the difference between the plasmatic estradiol levels during the climacteric stage that is related to the establishment of the depression disease and the antidepressant responses. We have also mentioned that estradiol slows the clearance of 5-HT and at the same time disables the same effect produced by fluvoxamine per se. In this sense during the rat estrous cycle, it has been shown that both estrous and diestrus phases are characterized by low estradiol levels in comparison to the proestrous phase; the fluvoxamine increases the clearance time of 5-HT, but not in the proestrous phase [41]. Rats with 2–3 postovariectomy weeks, it is observed that fluvoxamine increases the clearance time of 5-HT, the same effect caused by the estradiol benzoate treatment. However, the pretreatment with estradiol benzoate blocks the fluvoxamine effect [41].

Additionally evaluated the estradiol effect on the 5-HTT functionality, through time a clearance of the 5-HT, in different ages and postovariectomy time identifying that microinjection of 20pmol of estradiol on CA3 region in the hippocampus to inhibit 5-HTT in young adult rats (4 months age) after 2 weeks from the postovariectomy, but had not effect in middle-age rats (10 months), even with the use of <40 pmol dosage. While fluvoxamine reduces the clearance of 5-HT on rats about 10 months aged with 2 weeks, 4 and 8 months postovariectomy the same way as the 4 months rats [51]. Additionally, they detected that 5 μg/day of estradiol for 2 weeks subcutaneously via implantation of osmotic minipumps produces antidepressant effects on forced swim test on 4-month aged rats but not in 10-month aged rats both with 2 weeks of postovariectomy. Nevertheless the dosage of estradiol for 10 μg/day produces an antidepressant effect after 2 weeks of the postovariectomy procedure, but not at 4 months of postovariectomy in 10-month aged rats. The same dosages produced the same antidepressant effect on older rats (14 months of age) after 2 weeks of postovariectomy. The authors conclude that the lack of an antidepressant effect in estradiol is due to the 4-month hormone withdrawal and not to an age effect. Also in the same study, they reported that 2 weeks of treatment with sertraline, an antidepressant selective serotonin reuptake inhibitors (SSRI), on rats from 4 to 10 months of age with 2 weeks, 4 months, and 8 months of postovariectomy produce antidepressant effect in the forced swim test. In this study, it is concluded that the age influences the potency of estradiol on the 5-HTT, but its effects were strongly reduced if the period of postovariectomy is longer. On the other hand, the treatment with sertraline inhibited the 5-HTT and produced antidepressant-like effects without affected either by age or length of hormonal depletion [51].

In this context, the ERK signaling cascade is activated by antidepressant clinically effective as fluoxetine [44] and the systemic blockade of the MAPK pathway in mice produced depressive-like behavior in several animal models of experimental depression as well as inhibits the antidepressant effect of desipramine and fluoxetine in the forced swim test, a main model of depression [45]. On the other hand, the action of BDNF, which has been implicated in the mechanism(s) of action of the antidepressant (see Ref. [46]), is mediated through its high-affinity tyrosine kinase receptor B (TrkB), whose activation is required for

The acute intraventricular administration of IGF-1 produced antidepressant-like effects in mice evaluated in the tail suspension and forced swim tests [48], an effect detected after 3 days of the administration with participation of 5-HT [49]. The antagonism of the mGluR produced antidepressant-like effects in the forced swim test, probably through the intracellular signaling pathways described above [50]. Therefore, there is evidence about the interaction with the estrogens and the serotonergic system on the regulation on the depression disorder not only removing them but also influencing them by the other neu-

We have already mentioned the difference between the plasmatic estradiol levels during the climacteric stage that is related to the establishment of the depression disease and the antidepressant responses. We have also mentioned that estradiol slows the clearance of 5-HT and at the same time disables the same effect produced by fluvoxamine per se. In this sense during the rat estrous cycle, it has been shown that both estrous and diestrus phases are characterized by low estradiol levels in comparison to the proestrous phase; the fluvoxamine increases the clearance time of 5-HT, but not in the proestrous phase [41]. Rats with 2–3 postovariectomy weeks, it is observed that fluvoxamine increases the clearance time of 5-HT, the same effect caused by the estradiol benzoate treatment. However, the pretreatment with estradiol

Additionally evaluated the estradiol effect on the 5-HTT functionality, through time a clearance of the 5-HT, in different ages and postovariectomy time identifying that microinjection of 20pmol of estradiol on CA3 region in the hippocampus to inhibit 5-HTT in young adult rats (4 months age) after 2 weeks from the postovariectomy, but had not effect in middle-age rats (10 months), even with the use of <40 pmol dosage. While fluvoxamine reduces the clearance of 5-HT on rats about 10 months aged with 2 weeks, 4 and 8 months postovariectomy the same way as the 4 months rats [51]. Additionally, they detected that 5 μg/day of estradiol for 2 weeks subcutaneously via implantation of osmotic minipumps produces antidepressant effects on forced swim test on 4-month aged rats but not in 10-month aged rats both with 2 weeks of postovariectomy. Nevertheless the dosage of estradiol for 10 μg/day produces an antidepressant effect after 2 weeks of the postovariectomy procedure, but not at 4 months of postovariectomy in 10-month aged rats. The same dosages produced the same antidepressant effect on older rats (14 months of age) after 2 weeks of postovariectomy. The authors conclude that the lack of an antidepressant effect in estradiol is due to the 4-month hormone withdrawal and not to an age effect. Also in the same study, they reported that 2 weeks of treatment with sertraline, an antidepressant selective serotonin reuptake inhibitors (SSRI), on

antidepressant-like effect [47].

72 A Multidisciplinary Look at Menopause

rotransmitter systems and other kinds of receptors.

benzoate blocks the fluvoxamine effect [41].

In support to clinics finding about 5-HT2A receptors above mentioned some animal studies it has been observed that the administration of 5-HT2A receptor antagonist, i.e., ketanserin (0.1 mg/kg, i.p., 14 days) produces antidepressant effects in forced swim test and anxiolytic effect in elevated plus-maze test both in the proestrous and estrous phases of estrous cycle, characterized by high concentrations of progesterone and estradiol. In contrast, produces anxiogenic effect in phases with reduce concentrations of estradiol [52]. It is suggested that 5-HT2A receptors play different roles on the modulation of anxiety and depression associated with the alterations of hormonal concentrations during the ovarian cycle. In contrast, ketanserin administered in the same doses (0.1 mg/kg, i.p.) for 7 days in male rats produces an antidepressant-like effect, and together with the antidepressant fluoxetine (5 mg/kg, i.p., 7 days), it potentiates the antidepressant effect in forced swim test [53]. This suggests that the effect of ketanserin on females goes beyond changes in hormonal concentrations, which requires exploration.

Previous searches suggest that different hormonal levels, which vary through different reproductive statuses on women, may cause some changes on serotonergic system. For example, density and potential binding of the 5-HT1A and 5-HT2A receptors, as well as the potential binding of the 5-HTT in different brain structures linked to the mood changes, may contribute to the depression establishment. Those disruptions on the serotonergic system may influence or modify negatively the success of therapeutic response treated with antidepressant drugs or HRT; there is one possibility that must be explored.

### **5.1. Pharmacological response prediction: 5-HT1A and 5-HT2A receptors**

Pharmacological compounds that take action on 5-HT1A receptors such as SSRI are clinically effective antidepressants but require a period of 3–6 weeks of treatment to establish the therapeutic effects [54]. Additionally, 50 to 70% depressed patients respond to the first pharmacological treatment, and less than 40% get a total remission [54]. Combination of SSRI with 5-HT2A receptor antagonist makes the latency period shorter for the establishment of antidepressant effect [55]. This fact suggests that the stimulation of 5-HT1A receptors by SSRI and the inactivity of 5-HT2A receptors, which are part of the serotonin release on limbic areas, produce synergism effect. Therefore, the alteration in the expression of receptors in different brain areas, associated with variations of hormones such as estradiol, mainly in the stages of the climacteric, can influence the pharmacological response to antidepressants.

There are controversial data related to regulatory mechanism, which are exerted to antidepressant treatments on the 5-HT1A and 5-HT2A receptor density. A study developed by Kranz et al. [56] did not detect differences on the 5-HT1A receptor density on structures such as the hippocampus, the frontal cortex, and the raphe on postmenopausal woman [56]. After the administration of HRT with 17β-valerate ester alone or combined with progesterone, no matter the fact exist, a significant increase of estradiol and progesterone, an effect that has been identified on postmenopausal women [28]. This suggests that plasma concentrations of estradiol that are still elevated in premenopausal women compared to postmenopausal women seem to determine the 5-HT 1A receptor expression on the estrogenic treatment response.

### **6. Final comments and conclusion**

Variations in the levels of ovarian hormones that occur throughout the stages of climacteric and postmenopause severely impact women's mood. The depression is found mainly in the stages with continuous hormonal oscillations like perimenopause and premenopause. However, the relationship between hormonal and serotonergic systems in the climacteric and postmenopausal stages needs to be explored. The neurochemical and neurophysiological modification consequence of the oscillating hormonal levels leads to alterations in the cerebral neurotransmission functioning, mainly on the serotonergic system of the 5-HTT, 5-HT turnover, and 5-HT1A/5-HT2A receptors. This affects the pharmacological response to antidepressant treatments, both with estrogen therapy and with SSRI or tricyclic drugs in the different climacteric and postmenopausal stages.

The limitation on the studies have contributed to the establishment of these hypothesis emerged by the reduced length of women included in the studies and the wide range of ages which is used, because these incorporate women who are in different stages and different reproductive status and also women going through induced oophorectomy postmenopausal on early ages. Also, the lack of quantification of the hormonal levels, principally estradiol, FSH, and the ovarian function markers such as inhibin B, antral follicle count, anti-Müllerian hormone, and the estradiol levels. There is a direct relationship between advanced age and elevated serum basal levels which is associated with poor ovarian response. However, additional studies are needed to support these findings because it should let us categorize effectively those women on their reproductive stage. Thus, it allows us to establish a correct reciprocity between the serotonin changes and evaluated stages.

In addition, some limits in the imaging studies (e.g., PET), which are difficult to correct analysis on small brain structures or markers used, are not always selective to serotonin receptors, principally 5-HT2A receptors. It is also necessary to extend the researches related to serotonin changes on women with some depressant disorder, as major depression on all the reproductive stages, because some recent studies are only used to evaluate the symptomatology improvement on menopause, as somatic, urogenital, or physiologic symptomatology. On the last one, the symptomatology causes low motivation but without depression diagnosis, which limits the exploration of the neurochemical alterations that underlay to the depressive disorder on many different reproductive stages.

There are two areas that have been explored yet; the first one is nonsymptomatic women, thus, probably related to the hormonal levels through the reproductive stages and the correlation with brain serotonergic function, and also women through oophorectomies on early ages or ovarian failure (both under 40 years old). Women through an abrupt fall on ovarian hormone and some studies point out a high prevalence of depressive disorder longer and severe. Data may contribute to possible genetic factors, biological, psychosocial, and environmental, which are related to the establishment of the depressive disorder on different climacteric and postmenopausal stages.

In conclusion, depression associated to climacteric and postmenopausal stages involves changes in the serotonergic system, which includes an increase in the 5-HT clearance, turnover of 5-HT, and affinity of 5-HTT, as well as increased expression of 5-HT1A and 5-HT2A receptors in different brain regions (i.e., prefrontal cortex and hippocampus). All these changes seem to be a result of the oscillations in the ovarian hormone concentration characteristics of the climacteric and postmenopausal stages.

### **Conflicts of interest**

Kranz et al. [56] did not detect differences on the 5-HT1A receptor density on structures such as the hippocampus, the frontal cortex, and the raphe on postmenopausal woman [56]. After the administration of HRT with 17β-valerate ester alone or combined with progesterone, no matter the fact exist, a significant increase of estradiol and progesterone, an effect that has been identified on postmenopausal women [28]. This suggests that plasma concentrations of estradiol that are still elevated in premenopausal women compared to postmenopausal women seem to determine the 5-HT 1A receptor expression on the estrogenic treatment response.

Variations in the levels of ovarian hormones that occur throughout the stages of climacteric and postmenopause severely impact women's mood. The depression is found mainly in the stages with continuous hormonal oscillations like perimenopause and premenopause. However, the relationship between hormonal and serotonergic systems in the climacteric and postmenopausal stages needs to be explored. The neurochemical and neurophysiological modification consequence of the oscillating hormonal levels leads to alterations in the cerebral neurotransmission functioning, mainly on the serotonergic system of the 5-HTT, 5-HT turnover, and 5-HT1A/5-HT2A receptors. This affects the pharmacological response to antidepressant treatments, both with estrogen therapy and with SSRI or tricyclic drugs in the

The limitation on the studies have contributed to the establishment of these hypothesis emerged by the reduced length of women included in the studies and the wide range of ages which is used, because these incorporate women who are in different stages and different reproductive status and also women going through induced oophorectomy postmenopausal on early ages. Also, the lack of quantification of the hormonal levels, principally estradiol, FSH, and the ovarian function markers such as inhibin B, antral follicle count, anti-Müllerian hormone, and the estradiol levels. There is a direct relationship between advanced age and elevated serum basal levels which is associated with poor ovarian response. However, additional studies are needed to support these findings because it should let us categorize effectively those women on their reproductive stage. Thus, it allows us to establish a correct reciprocity between the serotonin changes and evaluated

In addition, some limits in the imaging studies (e.g., PET), which are difficult to correct analysis on small brain structures or markers used, are not always selective to serotonin receptors, principally 5-HT2A receptors. It is also necessary to extend the researches related to serotonin changes on women with some depressant disorder, as major depression on all the reproductive stages, because some recent studies are only used to evaluate the symptomatology improvement on menopause, as somatic, urogenital, or physiologic symptomatology. On the last one, the symptomatology causes low motivation but without depression diagnosis, which limits the exploration of the neurochemical alterations that underlay to the

There are two areas that have been explored yet; the first one is nonsymptomatic women, thus, probably related to the hormonal levels through the reproductive stages and the correlation with

**6. Final comments and conclusion**

74 A Multidisciplinary Look at Menopause

different climacteric and postmenopausal stages.

depressive disorder on many different reproductive stages.

stages.

The authors declare no conflicts of interest.

### **Acknowledgements**

The present chapter was part of the postdoctoral activities linked to the strengthening of the quality of the national postgraduate that the first author made in the Centro Universitario de los Lagos of the University of Guadalajara with fellowships from the Consejo Nacional de Ciencia y Tecnología (CONACyT, CVU: 210315, SNI: 64200).

### **Author details**

Rosa Isela García-Ríos1 \*, Armando Mora-Pérez2 and Cesar Soria-Fregozo2

\*Address all correspondence to<EMAIL_ADDRESS>
1 Department of Biomedics, University Center of Tonalá, University of Guadalajara, Tonalá, Jalisco, México

2 Laboratory of Psychobiology and Molecular Biology, University Center of Los Lagos, University of Guadalajara, Lagos de Moreno, Jalisco, México

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**3.5 DNA strand breaks**

 These injuries are divided based on the breaking of one or both strands. Single strand breaks (SSBs) can be generated by normal cellular procedures that went wrong, such as erroneous or abortive activity of DNA topoisomerase I (Top1), which presents mitochondrial localization, and when it fails may produce proteinlinked DNA breaks [23], also SSBs are produced by ineffective base excision repair (BER), or by oxidative stress [24]. One lesion related to SSBs is the formation of a covalently linked AMP to a 5′ phosphate, product of an unsuccessful DNA ligase activity [25]. On the other hand, double strand breaks (DSBs) are the most harmful, since they can provoke global cellular responses that involve many aspects of cell metabolism [26]. These lesions may occur by endogenous agents like reactive oxygen species (ROS), errors in DNA metabolism by topoisomerases, and nucleases or detention of replisome. On the other hand, lesion can be caused by exogenous insults such as ionizing radiation and chemotherapeutic drugs [1].


**1. Introduction**

Recent years have seen a growing interest in ultra-low-voltage operational transconductance amplifiers (OTAs) [1–18] that are a key building block in many analog and mixed-signal applications such as Internet-of-Things (IoT) and biomedical ones [19–22]. This is a strong incentive to innovate the design flow of analog blocks: even if they often constitute just a small fraction of a mixed-signal system, their design requires a large fraction of the overall effort. Indeed, both the schematic and layout design are typically carried out manually, iterating each step several times until specifications are met, also taking into account the required robustness under process, supply voltage and temperature (PVT) variations. To minimize the analog design effort and hence the cost and time-to-market of such mixed-signal applications, circuit solutions for analog blocks based on digital standard cells were explored in [23,24]. The end goal is to achieve a fully automatic design flow for the analog blocks that is similar to the one adopted for the digital section; as an intermediate step, the use of digital standard cells to design analog functions allows for the automating of the place and route steps of the design flow and, in perspective, the achievement of a fully automatic synthesis flow for both analog and digital blocks.

Recently, different approaches to exploit digital-based architectures to mimic the behavior of analog functions were explored in [25]. In particular, the behavior of OTAs has been mimicked through VCO-based architectures [26–28] and the DIGOTA approach [29–31]. Even if all these innovative techniques are very interesting from a research point of view, the most common approach to implementing analog building blocks suitable for automatic place and route exploits the digital standard cells as basic analog amplifiers [32–37]. In fact, the simplest digital gate (the inverter) behaves as a common source amplifier [38], and several inverter-based OTAs [39–50] have been proposed in the literature. However, differently from custom-designed inverters, the standard-cell inverter is typically optimized for area footprint or symmetrical slew rate, and as a consequence, it exhibits a systematic offset in its input–output dc transfer characteristic which impacts the output static voltage and

**Citation:** Centurelli, F.; Della Sala, R.; Scotti, G. A Standard-Cell-Based CMFB for Fully Synthesizable OTAs. *J. Low Power Electron. Appl.* **2022**, *12*, 27. https://doi.org/10.3390/ jlpea12020027

Academic Editor: Orazio Aiello

Received: 28 February 2022 Accepted: 27 April 2022 Published: 5 May 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

strongly degrades the performance of standard-cell-based cascaded amplifiers. According to the above considerations, the design of standard-cell-based OTAs must cope with additional issues that make achieving good and robust performance a very critical task. Several authors [37,42,50–52] have pointed out that the performances and even the operation of standard-cell-based analog circuits are severely impaired by PVT and mismatch variations, resulting in incorrect bias, large offsets and significant performance variations.

In such a context, the use of a common-mode feedback (CMFB) loop for each differential gain stage becomes mandatory to ensure a stable bias point [53–55], especially for ultra-low-voltage applications. The need to design a standard-cell-based CMFB greatly restricts the design options; some CMFB solutions have been proposed in the literature, but they usually do not involve an explicit reference voltage, resulting in some sensitivity to process, supply voltage and temperature (PVT) variations.

In this paper, we propose a fully standard-cell-based CMFB loop that exploits an explicit reference voltage to guarantee robust biasing, and we exploit it to design a twostage OTA. Thanks to the proposed approach, a stable dc output voltage is guaranteed for the first stage, allowing a correct biasing of the second stage. The paper is structured as follows: in Section 2, the proposed CMFB is described and analyzed; in Section 3, the design of the standard-cell-based OTA is presented. Section 4 reports the simulation results, and, finally, conclusions are drawn in Section 5.

#### **2. The Proposed CMFB**

Figure 1a shows a CMOS inverter that can be thought of as a common-source amplifier. Its dc output voltage depends on the size of NMOS and PMOS devices and is also affected by PVT and mismatch variations. Figure 1b shows the dc input–output transfer characteristic (blue dashed line) and its derivative (continuous green line) for a typical standard-cell inverter, as a function of the input bias voltage Vi for a supply voltage *VDD* = 0.3 V. Figure 1b clearly shows that an incorrect input dc bias results in a drop of voltage gain, thus making multistage amplifiers very difficult to implement if the dc output voltage of basic inverter stages is not controlled. The plot in Figure 1b also highlights the systematic offset of the inverter from a standard-cell library. In fact, the maximum gain is achieved for an input bias voltage different from *VDD*/2 = 150 mV (value marked as a red dashed line). This systematic offset of the inverter (resulting in a logic threshold different from *VDD*/2) is due to the fact that standard cells are not optimized for analog applications, and a trade-off between area, propagation time and balancing constraints is considered.

**Figure 1.** CMOS inverter (**a**) and its dc gain vs. input dc voltage (**b**).

A fully differential amplifier can be easily obtained using two inverters; however, it requires a CMFB loop to reduce the common-mode gain and to control the dc output voltage. Furthermore, to ensure correct biasing, multi-stage fully differential amplifiers require a CMFB at each stage. In the absence of accessible terminals to set the bias point of the inverter (e.g., the gate or body terminals of individual devices), the CMFB typically

exploits two inverters with shorted outputs to sense the common-mode output voltage and other inverters as current sources to close the loop at the input of the main amplifier [53–55]. However, when applied to the first stage, this technique adds a resistive component to the input impedance of the OTA, and, therefore, the use of common-mode feedforward [33] has been proposed as an alternative. It is worth noting that, typically, this approach is used to reduce the common-mode gain, whereas other techniques such as body biasing [34,53] are exploited to set the output dc common-mode voltage. However, ultra-low voltage applications show low tolerance to biasing errors, and when standard-cell inverters are used, the body terminal is often not available for biasing purposes.

To maintain the advantages of the feedback avoiding this drawback, one option is to use a local common-mode feedback (LCMFB): when applied at transistor level [17], the LCMFB is typically implemented with a pair of common-mode sensing resistors whose central node is connected to the gates of the active load devices. The corresponding standard cell implementation [37] exploits a pair of sensing inverters and a pair of controlling inverters connected to the same output nodes. For the differential mode signal, the load impedance of the LCMFB is the output resistance of the loading inverters, whereas for the common-mode signal the LCMFB provides a low impedance load that reduces the gain, improving the common-mode rejection ratio (CMRR).

In this work, in order to improve the robustness of the dc operating point to PVT variations and to overcome the systematic offset of the standard cell inverters, we propose to add an explicit voltage reference *Vref* to the standard-cell LCMFB through the inverter *I*7, as shown in Figure 2.

**Figure 2.** Topology of the standard-cell-based OTA with the proposed CMFB.

The resulting fully differential amplifier topology is depicted in Figure 2 (indicated as *First-Stage*): different colors are used to highlight the inverters constituting the gain stage (*I*1 and *I*1*'*), the common-mode estimator (*I*2, *I*2*'* and *I*3), the reference inverting buffer (*I*7, loaded by *I*5) and the CMFB auxiliary amplifier (*I*4, *I*5, *I*6 and *I*6*'*). Inverters with their input and output terminals connected together are used as load devices to avoid high impedance nodes in the loop, providing better stability and a degree of freedom to design the circuit, as will be shown following this section. They are equivalent to parallel NMOS and PMOS diode-connected devices; thus, the cascade of an inverter and such a diode-connected inverter is equivalent to the parallel connection of an NMOS and a PMOS diode-loaded common-source stage.

To analyze the proposed topology and obtain design guidelines, we model each inverter *IX* (*X* = 1, ... , 7) with a transconductance gain *GX* and an output conductance *GoX*, given by

$$G\_{\mathcal{X}} = \mathcal{g}\_{mn\mathcal{X}} + \mathcal{g}\_{mp\mathcal{X}} \tag{1}$$

$$G\_{oX} = \mathcal{g}\_{dsu}\chi + \mathcal{g}\_{dspX} \tag{2}$$

where *gm* and *gds* are the small-signal transconductance and output conductance of MOS devices, and *n* and *p* subscripts refer to NMOS and PMOS transistors, respectively. We assume that they scale linearly with the size of the devices (hence with the strength of the standard cells, *IV\_xN* meaning an inverter whose devices have *N* times the minimum width), and their ratio is the voltage gain *AX* = *GX*/*GoX* that we assume is identical for all the inverters (hence AX = A for x = 1, . . . , 7).

Let *α* be the ratio of the strengths of inverters *I*6 and *I*1 (hence *α* = *G*6/*G*1), *λ* = *G*2/*G*3, *ρ* = *G*4/*G*5 and *β* = *G*7/*G*4. The differential voltage gain of the first stage in Figure 2 results in

$$A\_d = \frac{A}{1+a} \tag{3}$$

where the loading effect of the LCMFB is considered. For the common mode, the analysis provides

$$V\_{\infty} = A\_c V\_{ic} + A\_R V\_{ref} \tag{4}$$

where *Vic* and *Voc* are the input and output common-mode components. The gains are

$$A\_{\mathfrak{L}} = \frac{A}{(1+\mathfrak{a})D} = \frac{A\_d}{\mathbb{C}MRR} \tag{5}$$

$$A\_{\mathbb{R}} = \frac{\alpha A \beta \rho \varepsilon\_{4}}{(1+\alpha)D} \tag{6}$$

$$D = 1 + \frac{2\alpha A \lambda \varepsilon\_2 \rho \varepsilon\_4}{1 + a} \tag{7}$$

where the error factors

$$x\_2 = \frac{1}{1 + \frac{2\lambda + 1}{A}}\tag{8}$$

$$\varepsilon\_4 = \frac{1}{1 + \frac{\beta \rho + \rho + 1}{A}} \tag{9}$$

take into account the effect of the output conductances (ideally, if *GX* >> *GoX,*, since *A* approaches to infinite, the values of *ε*2 and *ε*4 tend to 1).

Equations (3)–(9) show that the CMRR of the stage is set by *D* in (7) and allow the ability to derive design guidelines for the choice of the inverter sizes. A trade-off between high CMRR and low gain penalty due to the loading effect involves the factor *α*: a large value of *α* maximizes the CMRR, whereas the smaller its value, the lower the reduction of the differential gain (3). A suitable solution is to choose *α* = 1 and maximize the CMRR acting on the other factors.

Correct biasing would require *AR* = 1, which in the limit of large CMRR implies

$$
\beta = 2\lambda \varepsilon\_2. \tag{10}
$$

CMRR optimization then requires maximizing

$$
\beta \rho \varepsilon\_4 = \frac{\beta \rho}{1 + \frac{\beta \rho + \rho + 1}{A}}.\tag{11}
$$

that asymptotically tends to *A* for increasing *β* and *ρ*. Moreover, by (7) and the condition (10), we obtain

$$
\lambda = \frac{\beta}{2} \frac{1 + 1/A}{1 - \beta/A} \tag{12}
$$

that poses the further design constraints. Equation (11) implies that the size of inverter *I*7 must be maximized, and (12) requires *β* < *A*.

In practical situations, the smallest inverter size to be used is limited by matching constraints (the smaller the transistors, the higher the standard deviation of mismatches, hence offset and common mode to differential mode conversion), and the largest inverter size is limited by area and power constraints and by available standard-cells. Hence, there is a limit to the size of *I*7 (that is *βρ* times larger than *I*5) and *I*2 (that is *λ* times larger than *I*3):

$$
\beta \rho \le \aleph\_{\text{max}} \qquad \lambda \le \aleph\_{\text{max}}.\tag{13}
$$

It must also be noted that there is a trade-off between CMRR and the common-mode range: a large value of λ provides a larger CMRR at the cost of the common-mode voltage swing at the output of the stage, since the output of *I*2 saturates.

From (12), setting a maximum value of *λ* poses a more stringent limit on the value of *β*:

$$\beta\_{\max} = \frac{2R\_{\max}}{1 + \frac{2R\_{\max} + 1}{A}}.\tag{14}$$

If *βmax* > *Rmax*, *βρ* is set to *Rmax* and maximizing (11) requires keeping the factor *ρ* as small as possible (*ρ* = 1). If *βmax* < *Rmax*, which is the case for low values of the gain *A*, *β* = *βmax* must be chosen; (11) then becomes

$$\frac{\beta\_{\max}\rho}{1 + \frac{\rho(\beta\_{\max} + 1) + 1}{A}}.\tag{15}$$

and its optimization involves maximizing *ρ*, whose maximum value is set by (13) to *Rmax/βmax*. A flow graph illustrating this design procedure is reported in Figure 3.

**Figure 3.** Proposed design approach for the CMFB.

Further insight into the behavior of the differential stage with the proposed CMFB can be gained by adding to the model of each inverter a current source *IoffX* that accounts for the offset of the inverter, i.e., the error in the output voltage with respect to *VDD*/2 when the input voltage is *VDD*/2:

$$I\_{offX} = \left. G\_{oX} V\_o \right|\_{V\_i = V\_{DD}/2}. \tag{16}$$

This current source accounts for both the systematic offset due to the design of the inverter (PMOS to NMOS size ratio) and the random variation due to mismatches, and we can assume it is proportional to the *strength* of the inverter. The resulting block scheme for the common-mode behavior of the stage is shown in Figure 4; if we consider the contribution to the output common-mode voltage *Voc* due to these offset current sources, which can be obtained by letting *Vic* = *Vref* = 0 in Figure 4, we obtain

$$V\_{oc}^{(wff)} = \frac{aA}{D(1+a)} \left[ \frac{I\_{off1} + I\_{off6}}{aG\_1} + \frac{\mu \varepsilon\_2}{G\_3} \left( 2I\_{off2} + I\_{off3} \right) - \frac{\varepsilon\_4}{G\_5} \left( I\_{off4} + I\_{off5} + I\_{off7} \right) \right]. \tag{17}$$

Equation (17) shows that the residual error on setting *Voc* = *Vref* is due also to the offset currents of the inverters and that the CMFB suppresses this error in the limit of its finite loop gain. This is true both for the systematic offset currents and for their random components, thus demonstrating that the circuit provides a stable dc output voltage under process and mismatch variations. It must be noted that a suitable choice of the inverter strengths can lead to minimizing (17) and could be used as a further design constraint for design optimization.

**Figure 4.** Model for the common-mode half circuit of the proposed CMFB loop considering the offset of the inverters.

### **3. Standard-Cell-Based OTA**

An operational transconductance amplifier must provide high voltage gain, thus requiring, especially in an ultra-low-voltage environment with deep submicron technologies, the cascade of at least two gain stages with a differential-to-single-ended (D2S) conversion.

In the context of a standard-cell-based approach, mimicking the typical analog architecture with an input D2S converter followed by single-ended gain stages would result in a very poor CMRR and in a very high sensitivity to PVT variations. Better performance can be achieved by exploiting differential stages with CMFB loops to improve the CMRR and stabilize the bias point, followed by a final D2S stage.

To illustrate this approach, we propose a two-stage OTA, shown in Figure 2, composed by the fully differential stage described in the previous section (*First-Stage*) followed by a standard-cell-based D2S converter (*Second-Stage*), composed by inverters *I*8–*I*11. Inverters *I*8 and *I*9 constitute an inverting voltage buffer whose gain is ideally −1, and inverters *I*10 and *I*11 act as transconductance amplifiers driving the same output node.

The voltage gain of the D2S stage is thus ideally

$$\frac{V\_{out}}{V\_{o1p} - V\_{o1m}} = A\_{d2} = \frac{A}{2}.\tag{18}$$

with an infinite CMRR. However, in deep submicron technologies the voltage gain *A* is limited; hence, the output conductances of *I*8 and *I*9 cannot be neglected in the analysis. This reduces the gain of the voltage buffer and drastically worsens the CMRR even in

typical conditions. Assuming *I*8 = *I*9 and *I*10 = *I*11, differential and common-mode gains of the second stage are

$$A\_{d2} = \frac{A}{2} \frac{1 + 1/A}{1 + 2/A} \tag{19}$$

$$A\_{c2} = \frac{A}{2} \frac{2/A}{1 + 2/A} = \frac{1}{1 + 2/A} \tag{20}$$

and the overall CMRR results are

$$\text{CMRR}\_{\text{TOT}} = \frac{A\_{VD}}{A\_{V\text{C}}} = \frac{A\_d A\_{d2}}{A\_{\text{c}} A\_{\text{c2}}} = D \frac{A+1}{2} \tag{21}$$

where *D*, defined in (7), is the CMRR of the first stage.

The D2S stage presents an output pole set by the load capacitance CL; moreover, its dual path nature results in a pole–zero doublet similar to that provided by the current mirror load of a differential pair. With reference to Figure 2, assuming *I*8 = *I*9 and *I*10 = *I*11 and considering a differential input to the D2S (i.e., *Vo*1*p* = −*Vo*1*m*), the frequency response of the D2S can be written as

$$A\_{d2} = \frac{A}{2} \frac{2\left(1 + 1/A\right)\mathcal{G}s + s\mathcal{C}\_X}{(1 + 2/A)\mathcal{G}\_\mathcal{S} + s\mathcal{C}\_X} \frac{1}{1 + s\mathcal{C}\_\iota / 2\mathcal{G}\_{\iota 10}}\tag{22}$$

where *CX* is the total capacitance seen at the output of *I*8. Equation (22) shows that the pole and zero due to the inverting buffer *I*8–*I*9 are spaced by an octave; thus, their effect can be neglected. It must further be noted that Equation (22) poses no constraint on the sizing of inverters *I*8 and *I*9 with respect to *I*10 and *I*11; regardless, it could be convenient to use inverters of the same size to provide a symmetric loading to the first stage.

The OTA is stable when driving a sufficiently large load capacitance that makes the output pole dominant; for small load capacitors, a compensation is needed. More in detail, neglecting the pole–zero doublet due to *I*8 and *I*9, the internal pole of the OTA is given by

$$p\_{int} = \frac{G\_{o1}(1+a)}{C\_{in2} + C\_{in8}} \tag{23}$$

where *Cin*2 and *Cin*8 are the input capacitances of *I*2 and *I*8, and the output pole is

$$p\_{out} = \frac{2G\_{o10}}{C\_L} \tag{24}$$

(assuming *I*10 = *I*11). By imposing that the second pole is *γ* times the unity-gain frequency (where *γ* is set by the required phase margin), the minimum load capacitance required to have stability with the dominant pole at the output is

$$\mathbb{C}\_{Lmin} = \gamma \frac{2G\_{o10}A\_{VD}}{p\_{int}} = \gamma \frac{A^2}{4} \frac{G\_{o10}}{G\_{o1}} (\mathbb{C}\_{in2} + \mathbb{C}\_{in8}) \tag{25}$$

where *α* = 1 has been considered. Equation (25) shows that the standard-cell-based OTA has the capacity to drive small capacitors, as required in most on-chip applications, without the need of compensation capacitors thanks to the fact that the intrinsic gain of inverters is low and small-size inverters are used in the output stage. The latter condition, however, limits the slew rate of the OTA.

#### **4. Simulation Results**

The OTA in Figure 2 was designed using the standard-cell library of the STMicroelectronics 130 nm CMOS technology. Supply voltage was set to 0.3 V. Taking into account the design guidelines in Section 2 and the mismatch requirements that impose the use of non-minimum size cells, the inverters were designed as specified in Figure 2 (inverter *IV\_xN* has devices with *N* times the minimum width). It must be noted that the low voltage

gain of the inverters (*A* = 19 dB) result in the error factors (8) and (9) that are significantly below 1: in particular, we obtain *ε*2 = 0.5 and *ε*4 = 0.6. With reference to the analysis in Section 2, the smallest inverters were chosen as 20 times the minimum size inverter (*IV\_x20* for all the inverters except *I*2 and *I*8) and the design factors were set to *α* = 1, *λ* = 4, *ρ* = 1 and *β* = 4. The resulting static offset is therefore

$$V\_{oc}^{(inff)} = 0.57 \frac{I\_{off1}}{G\_{o1}}.\tag{26}$$

To assess the effectiveness of the proposed approach in stabilizing the dc output voltage, the pseudo-differential stage with the CMFB was tested under PVT variations. The reference voltage was set to *VDD*/2, and the error of the output dc common-mode voltage with respect to this reference was evaluated. The LCMFB without *I*7 and the reference input were also tested for comparison.

Figure 5 shows the relative error on the dc output common-mode voltage for the proposed CMFB and for the LCMFB without the reference input, under variations of temperature and supply voltage. An error is present in typical conditions (300 mV VDD, 27 ◦C) due to the finite loop gain of the CMFB. When the reference input is present, the output common-mode voltage presents a limited variation when the temperature ranges from 0◦ to 80 ◦C, whereas the voltage drifts with the temperature if the reference input is not used. For what concerns the variation of the supply voltage, the dc common-mode output voltage tracks *VDD*/2 with an error, due to the finite loop gain, that presents little variation and is lower than the error achieved by the design without the reference input.

**Figure 5.** Relative error of the dc output common-mode voltage vs. temperature and supply voltage.

The advantage provided by the reference input is even more evident when the effect of process variations is considered. Figure 6 shows the relative error on the dc output common-mode voltage with respect to the reference input for the extreme process corners. A residual error of about 1.34% is reported in typical (TT) conditions due to the finite loop gain of the CMFB. This error increases in the corners where NMOS and PMOS devices present opposite variations (corners FS and SF); however, the values are below 10% and are one third of the errors obtained if the reference input is not used.

**Figure 6.** Relative error (%) of the dc output common-mode voltage vs. process corners; darker colors correspond to higher relative errors.

The proposed pseudo-differential stage with CMFB thus results in suitable-to-design multi-stage amplifiers, and the OTA in Figure 2 was designed and simulated. The amplifier dissipates 4.4 μW from a 0.3 V supply; this relatively high power consumption is due to the use of large inverters to minimize the mismatches. Figure 7 shows the differential (*AVD*) and common-mode (*AVC*) gains of the OTA loaded by a 1.5 pF capacitor. The differential dc gain is 28.27 dB with a 15.42 MHz unity-gain frequency and 54.18◦ phase margin; the common-mode rejection ratio (CMRR) is about 41.07 dB and is constant across all the bandwidth.

The amplifier was tested in a unity-gain buffer configuration to assess its large-signal performance. The response to an input pulse from 45 to 255 mV (Figure 8) shows identical values for positive and negative slew rates equal to 9.75 V/μs. We also simulated the unitygain buffer configuration with a 1 MHz sinusoidal input applied, and Figure 9 reports the total harmonic distortion (THD) as a function of the input amplitude. Distortions below 1% (−40 dB THD) are obtained for an input amplitude up to 115 mV, which is about 75% of the rail-to-rail swing.

Figure 10 shows the input-referred noise spectrum of the OTA: a noise corner frequency lower than 1 kHz with a white noise spectral density of 0.497μV/√Hz measured at 10 kHz was obtained, resulting in 1.445 mV rms noise when integrated over the whole closedloop bandwidth.

**Figure 7.** Differential (red) and common-mode (blue) gain of the proposed OTA.

**Figure 8.** Response of the OTA in unity-gain configuration to a 45-to-255 mV input step.

**Figure 9.** Total Harmonic Distortion vs. input amplitude for a 1 MHz sinusoidal input signal.

**Figure 10.** Input-referred noise spectrum of the OTA.

The performance under PVT variations and mismatches was evaluated to assess the robustness of the design. Table 1 reports the main performance parameters of the OTA in five different process corners highlighting how the proposed circuit exhibits a relatively low sensitivity to process variations. The effect of supply voltage and temperature variations is reported in Table 2: power consumption and gain-bandwidth product exhibit a nonnegligible variation as expected since there is no bias loop setting the currents. However, the voltage gain *AVD* and the output dc voltage (measured through the parameter *VOS*) are extremely stable, confirming the effectiveness of the proposed approach.

**Table 1.** Variations under process corners.

**Table 2.** Variations under supply voltage and temperature.

Table 3 reports the results of 200 Monte Carlo mismatch simulations that show a good robustness of the proposed OTA, with limited variation of all the parameters. As can be observed in Table 3, under mismatch variations, the standard deviation of the output offset voltage is 9.2 mV, in line with other ULV OTAs taken from the literature. In order to further reduce the standard deviation of *VOS* under mismatch variations, we can place multiple gates in parallel or exploit standard cells with larger driving capability, at the cost, however, of increased area and power consumption. We consider the proposed design as a good tradeoff between area, power consumption and output offset voltage standard deviation. Figure 11 shows the histogram of the CMRR, which is always higher than 10 dB and presents a log-normal distribution. The histogram shows that, even under mismatch conditions, acceptable values of CMRR are obtained, taking also into account the low value of the differential gain.

**Table 3.** Results of Monte Carlo mismatch analysis.

The layout of the proposed standard-cell OTA was generated by means of an automatic place and route flow by using the Cadence Innovus tool and is shown in Figure 12. The OTA occupies an area of 16.4 × 10 μm2 that is very limited, notwithstanding the use of large inverters to minimize the mismatches. The layout has been generated automatically starting from a Verilog netlist of the circuit, which is reported in the Appendix A.

**Figure 11.** Histogram of the CMRR for 200 Monte Carlo mismatch iterations.

**Figure 12.** Layout of the proposed OTA generated by using the Cadence Innovus automatic place and route flow.

Table 4 reports the comparison of the proposed OTA with other ULV OTAs from the literature. To compare the proposed OTA against state-of-the-art low-voltage amplifiers, we refer to the following commonly used figures of merit:

$$FOM\_S = \frac{GBW \ C\_L}{Pd} \tag{27}$$

$$FOM\_L = \frac{SR\_{AVG} \ C\_L}{Pd} \tag{28}$$

$$FOM\_{S,A} = \frac{GBW \ C\_L}{Pd \ Area} \tag{29}$$

$$FOM\_{L,A} = \frac{SR\_{AVG} \ C\_L}{Pd \ Area} \tag{30}$$

where *GBW* is the gain-bandwidth product, *CL* the load capacitance, *SRAVG* is the average slew rate and *Pd* is the power consumption. Subscripts S and L in (27) and (28) denote small signal and large signal, respectively, while the figures of merit (29) and (30) are normalized with respect to the layout area of the OTA. The comparison shows that the proposed circuit exhibits very good small signal performance and adequate large signal performance. Due to the very compact layout, the proposed OTA outperforms all other similar designs in terms of *FOML*,*A*. The proposed OTA also outperforms almost all other designs in terms of *FOMS*,*A*. Only [30] exhibits a higher *FOMS*,*A*; however, the OTA in [30] is made up of minimum-sized standard cells that result in high sensitivity to process variations and mismatches.

**Table 4.** Comparison with the literature.

STD = standard-cell-based; DIG s= DIGOTA; BD = body-driven; IB = inverter-based.

#### **5. Conclusions**

In this paper, we have presented a fully standard-cell-based common-mode feedback (CMFB) loop with an explicit voltage reference that allows the improvement of the CMRR of fully synthesizable standard-cell-based amplifiers and the stabilization of the dc output voltage with respect to PVT variations. A complete analysis of the circuit was presented to derive design guidelines. Simulations displayed that the use of an explicit reference input enhances the robustness of the CMFB to PVT variations.

The proposed CMFB was exploited to design a standard-cell-based OTA made up of only digital gates taken from a standard-cell library. The layout of the OTA was implemented by using a fully automated place and route flow by using the Cadence Innovus tool and starting from the Verilog netlist of the circuit. Simulation results illustrated very good values of both the small signal and large signal FOMs normalized to the area footprint of the circuits with a very good robustness of all the main performance parameters to PVT variations.

We remark that, due to the adoption of the proposed CMFB and to the design equations derived in this paper, the proposed standard-cell-based OTA results are more robust to PVT variations with respect to DIGITAL and standard-cell-based OTAs previously reported in the literature. However, it is worth noting that the performance attained by standard-cellbased OTAs is still less robust with respect to PVT and mismatch variations than that of OTAs designed with a custom analog design approach, which exhibit a well-defined bias current. Moreover, one of the main drawbacks of standard-cell single-ended OTAs is that the D2S converter (the last stage of the proposed OTA) cannot achieve good performance under PVT and mismatch variations, resulting in low and variable CMRR, thus reducing

the ICMR of the whole architecture. Therefore, one of the goals of future works will be to achieve better ICMR and CMRR performance by standard-cell D2S converters in order to enhance the performance of standard-cell-based OTAs.

**Author Contributions:** Conceptualization, F.C., R.D.S. and G.S.; methodology, F.C., R.D.S. and G.S.; software, R.D.S.; validation, F.C., R.D.S. and G.S.; formal analysis, F.C. and R.D.S.; investigation, F.C., R.D.S. and G.S.; data curation, R.D.S.; writing—original draft preparation, F.C.; writing—review and editing, F.C., R.D.S. and G.S.; visualization, R.D.S.; supervision, F.C. and G.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.