# Fully Differential Miller Op-Amp with Enhanced Large- and Small-Signal Figures of Merit

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## Abstract

**:**

_{L}= 1 MΩ and 7.3 for R

_{L}= 200 Ω.

## 1. Introduction

_{outpk}/I

_{totQ}< 0.5, where I

_{outpk}is the minimum of the positive and negative peak output currents: I

_{outpk}= MIN{I

_{outpk}

^{+}, I

_{outpk}

^{−}}. Most approaches to implement class AB output stages incorporate a floating battery between the gates of the output nMOS and pMOS transistors of a Miller op-amp. The popular class AB op-amps with floating batteries can be seen in [9,10]. A push-pull class AB op-amp [11,12,13] can be designed to drive both resistive and capacitive loads. However, the practical implementation of the floating battery is challenging in today’s sub-micron technology, where the supply voltage is a serious constraint. In order to maintain a well-defined constant output quiescent current, I

_{outQ}independent on supply voltage, nominal component values, and technology parameter variations, the floating battery scheme requires an additional I

_{outQ}control circuit. The control circuit can be complex and further increase the supply requirements and power dissipation, which can significantly lower the current efficiency.

_{Dyn}= SR.C

_{L}/P

_{Q}[14,15], where SR is slew rate, P

_{Q}is the quiescent power dissipation, and C

_{L}is load capacitance; (b) small-signal figures of merit FoM

_{SS}= f

_{u}.C

_{L}/P

_{Q}[14,16], where f

_{u}is the unity gain frequency; (c) and authors introduce a new large-signal static current efficiency figures of merit FoM

_{stat}= I

_{outp}

^{RL}/I

_{Qtotal}.

## 2. Proposed Op-Amp

_{u}in the proposed op-amp. As discussed in detail below, this approach offers several advantages with respect to conventional class AB schemes: it generates signal voltages V

_{Y}and V

_{YP}that are amplified versions and in phase with V

_{X}and V

_{XP}. In order to have enough headroom for the auxiliary amplifier’s input differential pair (M

_{4}, M

_{4P}), a floating battery V

_{SB}is used to reduce the threshold voltage of M

_{4}, M

_{4P}. This floating battery is implemented using a diode-connected PMOS transistor with a minimal quiescent current, just like V

_{BAT}in the input stage is used. In addition, M

_{4}and M

_{4P}are scaled up by a factor of three. This is to reduce their drain-source saturation voltage V

_{DSsat}. A resistive local common-mode feedback (RLCMFB) network is used as a load in order to obtain moderate gain A

_{Aux}from the AuxAmp. The non-inverting gain of the auxiliary amplifier is given approximately by ${A}_{Aux}=\left({V}_{Y}-{V}_{Y}{}_{P}\right)/{V}_{X}=\left({V}_{YP}-{V}_{Y}\right)/{V}_{XP}={g}_{m4,4P}{R}_{CMF}/2$. The AuxAmp increases the overall open-loop gain, the unity-gain frequency, and significantly the peak negative output currents and slew-rate of the op-amp. This AuxAmp also assists the proposed op-amp in maintaining an accurate output quiescent current I

_{OutQ}minimizing the effect of temperature, supply voltage variations, and technology parameter variations on I

_{OutQ}. The quiescent gate voltages V

_{Y}, V

_{YP}of transistors M

_{ON,ONP}control the quiescent output current I

_{outQ}. Under quiescent conditions, no current flows in resistors R

_{CMF}, and the gate-source voltage of M

_{ON,ONP}is V

_{Y}= V

_{YP}= V

_{GS5P,5Q}, independent of the value of R

_{CMF}that sets the gain A

_{Aux}. The AuxAmp consumes only 6% of the total op-amp quiescent current, which helps to keep the op-amp’s current efficiency high.

#### 2.1. Operation

_{X}decreases and at V

_{XP}increases, while the voltages at node V

_{Y}decrease and at node V

_{YP}increase by a factor A

_{Aux}. As a result, M

_{OP}will provide a large output positive current and M

_{ONP}a large negative output current. The drain currents of M

_{ON}, M

_{OPP}will decrease and eventually reach zero. Similarly, M

_{ON}can provide large negative output currents for negative input signals, and M

_{OPP}can provide large positive output currents as the voltage at V

_{XP}decreases. In the conventional floating battery scheme where variations V

_{X}, V

_{XP}are transferred directly to V

_{Y}, V

_{YP}, the maximum negative output current is limited by the relatively small positive excursion of V

_{X}, V

_{XP}transferred to V

_{Y}, V

_{YP}. In the proposed scheme, the gain A

_{Aux}increases significantly the excursion of V

_{Y}, V

_{YP}and the peak negative output current. A

_{Aux}also increases the open-loop gain, common-mode rejection ratio (CMRR), power supply rejection ratio (PSRR), and unity gain frequency of the op-amp.

#### 2.2. Frequency Response

_{I}is given by (1).

_{m}and r

_{o}are the transconductance gain and output resistance of all unit size NMOS and PMOS transistors, and R

_{X}is resistance at nodes V

_{X}, V

_{XP}.

_{Y,YP}is the resistance at nodes V

_{Y}and V

_{YP}: where ${R}_{Y}={r}_{o4P}.{g}_{mCP2P}.{r}_{oCP2P}\left|\right|{R}_{CMF}\left|\right|{r}_{o}{}_{5P}$. The value of the R

_{CMF}is selected in such a way so that ${R}_{CMF}\ll {r}_{o4}{}_{P},{r}_{oCP2P},{r}_{o5P}$. As a result, R

_{Y}can be approximated as R

_{Y}≈ R

_{CMF}. Thus, gain of the auxiliary amplifier can be expressed approximately by (2).

_{out}is ${R}_{out}={r}_{oOP}\left|\right|{r}_{oON}\left|\right|{R}_{L}$. g

_{mOP}and g

_{mON}are transconductance gains of output transistors M

_{OP}and M

_{ON.}

_{OLDC}of the proposed op-amp is expressed by (4).

_{X, XP,}and is given by (5).

_{X}is given by ${C}_{X}=\left(1-(-{A}_{out})\right){C}_{C}$.

_{out}is strongly dependent on R

_{L}. For very low R

_{L}values, it can even take values |A

_{out}| < 1. Besides the dominant pole, the proposed op-amp has two pairs of high-frequency poles: one at V

_{Y}(V

_{YP}) and another at V

_{outP}(V

_{outM}). The output high-frequency pole f

_{Pout}is given in (7).

_{Pout}to be higher than output pole frequency f

_{Pout_conv}of the conventional op-amp shown in Figure 2. The high-frequency output pole of the conventional op-amp of Figure 2 is given in (8).

_{mOP_conv}is the transconductance gain of the output PMOS transistor of the conventional op-amp. The value of f

_{Pout}of the proposed op-amp for C

_{L}= 300 pF and R

_{L}= 1 MΩ is 6 MHz, whereas the output pole frequency for the conventional-A op-amp f

_{Pout_conv}is only 687 kHZ for a similar loading condition.

_{Y}, V

_{YP}is expressed by (9).

_{Y}is given by ${C}_{Y}\approx {C}_{gsON}+{C}_{dBCP2P}+{C}_{dB5P}+{C}_{gdON}\left(1+\left(\raisebox{1ex}{${A}_{out}$}\!\left/ \!\raisebox{-1ex}{${A}_{VY}$}\right.\right)\right)+{C}_{gd5P}$.

_{PY}) at node V

_{Y,YP}depends on the value of R

_{CMF}. The high-frequency pole f

_{PY}is inversely proportional to the value of R

_{CMF,}i.e., ${f}_{PY}\propto 1/{R}_{CMF}$. Again from (2), it can be seen that the gain of the auxiliary amplifier depends on the value of R

_{CMF}, i.e., ${A}_{Aux}\propto {R}_{CMF}$. Thus, the selection of R

_{CMF}plays an essential role in determining the stability, overall open-loop gain, and slew-rate improvement of the proposed op-amp as the gain of the auxiliary control of the dynamic current of M

_{ON,ONP}. In the proposed circuit, the value of the R

_{CMF}is 60 kΩ. This selection of R

_{CMF}helps to place f

_{PY}at a higher frequency than the unity gain frequency of the op-amp. The higher value of f

_{pY}helps achieve approximately constant gain from the auxiliary amplifier until the proposed op-amp’s unity gain frequency. The value of the f

_{PY}in the proposed op-amp is 29 MHz, which is twice larger than the unity gain frequency of the proposed op-amp.

## 3. Results

_{in}and R

_{f}values of 100 kΩ were used in the simulation. Figure 6 shows the transient response of the proposed and Conv-A op-amps in unity gain inverting configuration for a 1 MHz, ±400 mVpp pulse input, with C

_{L}= 300 pF and two resistive load values R

_{L}= 200 Ω and 1 MΩ. From the pulse response, it can be seen that the Conv-A op-amp cannot follow the input pulse, whereas the proposed op-amp can follow the input for all the considered loading conditions. The proposed op-amp has a slew rate of 13 V/µs, whereas the Conv-A op-amp has a much lower slew rate of 0.9 V/µs. The proposed op-amp can provide ±4.36 mA peak currents to a 300 pF capacitor. On the contrary, the Conv-A op-amp can provide only 58 µA peak negative output currents, which corresponds to the class-A op-amp’s output quiescent current (I

_{outQ}). Figure 7 shows the single-ended output currents of both op-amps in the 200 Ω resistive load for ±400 mV pulse input. It can be seen that due to the substantial limitation of the negative current in the Conv-A op-amp, the outputs cannot follow the negative excursion of the input pulse. As a result, the op-amp cannot provide differential complementary output signals. It can be seen that the peak negative current is –58 μA. On the other hand, the proposed op-amp can provide complementary output signals with equal positive and negative output currents of ±1 mA in the 200 Ω resistive loads for the ±200 mV pulse input.

_{L}= 300 pF, 5 pF, and R

_{L}= 1 MΩ for the ±400 mVpp 1 MHz pulse input. The proposed op-amp can provide ±4.36 mA peak currents to 300 pF load capacitors. On the contrary, the Conv-A op-amp can provide only 58 µA negative output, which corresponds to the class-A op-amp’s output quiescent current (I

_{outQ}). Figure 9 shows the total harmonic distortion of the proposed and Conv-A op-amp for a 400 mV amplitude sinusoidal signal whose frequency is varied from 1 kHz to 8 MHz. It can be seen that the proposed op-amp has much lower (35 dB) harmonic distortion than the Conv-A op-amp.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 6.**Pulse response of the proposed and conventional op-amp, C

_{L}= 300 pF and R

_{L}= 1 MΩ and 200 Ω.

**Figure 7.**Single-ended transient current in R

_{L}= 200 Ω of the proposed and Conv-A op-amp for ±400 mV pulse input.

**Figure 8.**Output current of the proposed and conventional op-amp for C

_{L}= 300 pF, 5 pF and R

_{L}= 1 MΩ for the ±400 mVpp, 1 MHz pulse input.

**Figure 9.**THD of the proposed op-amp at different frequencies for 400 mV amplitude sinusoidal signal and R

_{L}= 200 Ω, C

_{L}= 300 pF.

**Figure 10.**Determination of close to rail-to rail output swing using a ±1.7 V, 0.5 MHz, triangular input signal.

Corner | tt | ff | fs | sf | ss | Std. |
---|---|---|---|---|---|---|

I (_{TotalQ}µA)
| 253 | 251 | 250 | 249 | 247 | 2 |

f (_{u}MHz)@ R_{L} =1 MΩ | 15.5 | 16.9 | 15.2 | 14 | 13.5 | 1.19 |

PM ()^{o}@ R_{L} =1 MΩ | 59 | 56 | 56 | 62 | 63 | 2.92 |

Gain | 117.9 | 114 | 117.6 | 118 | 117 | 1.5 |

SR (V/µs)
| 13 | 11 | 10 | 10 | 9 | 1.4 |

I_{outpk}^{−}R_{L} =200 Ω( mA)
| 2 | 1.9 | 1.9 | 2 | 2 | 0.05 |

Corner | tt | ff | fs | sf | ss | Std. |
---|---|---|---|---|---|---|

I (_{TotalQ}µA)
| 253 | 252 | 250 | 252 | 255 | 1.62 |

f (_{u}MHz)@ R_{L} =1 MΩ | 13.4 | 14.5 | 13 | 13.2 | 12 | 0.8 |

PM ()^{o}@ R_{L} =1 MΩ | 59 | 58 | 61 | 60 | 60 | 1.01 |

Gain (dB)
| 116.4 | 110 | 113 | 114.2 | 120 | 3.35 |

SR (V/µs)
| 13 | 12 | 11 | 12 | 14 | 1.01 |

I_{outpk}^{−} R_{L} =200 Ω( mA)
| 2 | 1.9 | 2 | 2 | 2 | 0.04 |

Corner | tt | ff | fs | sf | ss | Std. |
---|---|---|---|---|---|---|

I (_{TotalQ}µA) | 251 | 259 | 251 | 252 | 255 | 3.07 |

f (_{u}MHz)@ R _{L} =1 MΩ | 9.5 | 9.4 | 9.5 | 10 | 9.2 | 0.26 |

PM ()^{o}@ R _{L} =1 MΩ | 58 | 58 | 58 | 57 | 59 | 0.63 |

Gain (dB) | 100 | 95 | 111 | 110 | 117 | 7.9 |

SR (V/µs) | 11 | 14 | 11 | 12 | 15 | 1.62 |

I_{outpk}^{−}R_{L} =200 Ω( mA) | 2 | 1.8 | 1.9 | 2 | 2 | 0.08 |

Parameter (Units) | Proposed | Conv-A | [17] | [18] | [19] | [20] | [21] |
---|---|---|---|---|---|---|---|

Inversion Level | SI | SI | SI | SI | SI | SI | SB |

CMOS Process( µm) | 0.18 | 0.18 | 0.18 | 0.18 | 0.18 | 0.35 | 0.18 |

Supply Voltage (V) | ±0.9 | ±0.9 | 1.8 | 1.8 | 1.8 | 3.3 | ±300 |

Capacitive Load (pF) | 5–300 | 5–300 | 10 | 1 | 100 | 25 | 10 |

Resistive Load( Ω) | 1 M/200 | 1 M/200 | - | - | - | 500 | - |

SR( V/μs) | 13 | 0.9 | 17.83 | 650 | 63 | 248.6 | 8.4 |

DC Gain (dB) | 116.4/ 74.5 | 96.8/57.4 | 73 | 85.6 | 84 | 69.5 | 42.2 |

PM (º) | 59/82 @C _{L} = 300 pF, R_{L} = 1 MΩ/@C _{L} = 300 pF, R_{L} = 200 Ω | 57/90 | 64 | 66.7 | 77 | 69.65 | 54 |

f (_{u}MHz) | 13.32/11.21 | 3.88/4.2 | 15 | 987 | 91 | 354 | 16.1 |

CMRR @DC (dB) | 96 | 90 | 80 | 80 | - | 45 | 85.12 |

PSRR+ @DC (dB) | 95 | 87 | 78 | 78 | - | 27.5 | 53.25 |

PSRR-@DC (dB) | 92 | 85 | - | - | - | 56.89 | |

I (_{outpk} ^{+} _{RL}µA) | 2000 @200 Ω | 1500 @200 Ω | - | - | - | 2000 @500 Ω | - |

I_{outpk}^{−}_{RL =}_{200 Ω}( µA) | 2000 | 1500 | - | - | - | 0 | - |

I (_{totQ}µA) | 253 | 182 | 239 | 1000 | 1722 | 8042 | 41.3 |

Power (μW) | 455 | 327.6 | 429.68 | 1800 | 3100 | 26,540 | 24.8 |

Input Referred Noise | 317@1 kHz nV/√Hz | 330@1 KHz nV/√Hz | 84@100 kHz nV/√Hz | 118 µV_{rms}(1 Hz–100 MHz) | 340@100 kHz nV/√Hz | 35.52 @100 kHz | 69@1 MHz |

FOM_{CEDyn}( V.pF/µs.µW) | 8.6 | 0.82 | 0.41 | 0.4 | 2 | 0.23 | 3.39 |

FOM (_{SS}MHz.pF/µW) | 8.7/7.3 | 3.5/3.8 | 0.35 | 0.5 | 2.9 | 0.33 | 6.49 |

FOM_{CEStat}( µA/µW) | 7.9 | - | - | - | - | 0.08 | - |

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**MDPI and ACS Style**

Paul, A.; Ramirez-Angulo, J.; Vázquez-Leal, H.; Huerta-Chua, J.; Diaz-Sanchez, A.
Fully Differential Miller Op-Amp with Enhanced Large- and Small-Signal Figures of Merit. *J. Low Power Electron. Appl.* **2022**, *12*, 9.
https://doi.org/10.3390/jlpea12010009

**AMA Style**

Paul A, Ramirez-Angulo J, Vázquez-Leal H, Huerta-Chua J, Diaz-Sanchez A.
Fully Differential Miller Op-Amp with Enhanced Large- and Small-Signal Figures of Merit. *Journal of Low Power Electronics and Applications*. 2022; 12(1):9.
https://doi.org/10.3390/jlpea12010009

**Chicago/Turabian Style**

Paul, Anindita, Jaime Ramirez-Angulo, Héctor Vázquez-Leal, Jesús Huerta-Chua, and Alejandro Diaz-Sanchez.
2022. "Fully Differential Miller Op-Amp with Enhanced Large- and Small-Signal Figures of Merit" *Journal of Low Power Electronics and Applications* 12, no. 1: 9.
https://doi.org/10.3390/jlpea12010009