In this paper, the analytical approach of MOS transistor mismatch effect on common-mode gain of cross-coupled amplifier is presented. Transconductance (MOS transistor parameter) mismatch effect on common-mode gain of cross-coupled amplifier was analyzed. This study was started with mathematical derivation for representing the mismatch effect of transconductance between 2 differential pairs of crosscoupled amplifier due to common-mode voltage. The derivation result was simulated based on Monte Carlo simulation with random transconductance mismatch rate from 0.05% until 1%. The common-mode gain increases 36.9 dB and average common-mode gain is -81.1 dB. The transconductance mismatch rate increases followed by increase in common-mode gain. The results can be used by circuit designers to design analog circuits, especially operational amplifier used for biosignals processing to minimize the common-mode gain of their circuits. This research presents aid to circuit designers to improve their circuits performance

Abidin, Zainul

Maulana, Eka

Subroto, Ramadhani Kurniawan

Wijono, Wijono

English

TELKOMNIKA (Telecommunication Computing Electronics and Control)

TELKOMNIKA, Vol.17, No.1, February 2019, pp.448~452 
ISSN: 1693-6930, accredited First Grade by Kemenristekdikti, Decree No: 21/E/KPT/2018 
DOI: 10.12928/TELKOMNIKA. v17i1.11587   448 
  
Received July 2, 2018; Revised September 28, 2018; Accepted October 27, 2018 
Transistor mismatch effect on common-mode gain of 
cross-coupled amplifier 
 
 
Zainul Abidin*, Eka Maulana, Ramadhani Kurniawan Subroto, Wijono 
Electrical Engineering of Brawijaya University, MT Haryono St. 167 Malang, Indonesia,  
telp/fax: +62 341 554166 
*Corresponding author, e-mail: zainulabidin@ub.ac.id 
 
 
Abstract 
 In this paper, the analytical approach of MOS transistor mismatch effect on common-mode gain 
of cross-coupled amplifier is presented. Transconductance (MOS transistor parameter) mismatch effect on 
common-mode gain of cross-coupled amplifier was analyzed. This study was started with mathematical 
derivation for representing the mismatch effect of transconductance between 2 differential pairs of cross-
coupled amplifier due to common-mode voltage. The derivation result was simulated based on Monte 
Carlo simulation with random transconductance mismatch rate from 0.05% until 1%. The common-mode 
gain increases 36.9 dB and average common-mode gain is -81.1 dB. The transconductance mismatch rate 
increases followed by increase in common-mode gain. The results can be used by circuit designers to 
design analog circuits, especially operational amplifier used for biosignals processing to minimize the 
common-mode gain of their circuits. This research presents aid to circuit designers to improve their circuits 
performance. 
  
Keywords: biosignals processing, common-mode gain, cross-coupled amplifier, MOS transistor mismatch, 
transconductance 
  
Copyright © 2019 Universitas Ahmad Dahlan. All rights reserved. 
 
 
1. Introduction 
CMOS cross-coupled amplifier is frequently used in various application. For example, 
Fully Balanced Differential Difference Amplifier (FBDDA) is mainly constructed by using Cross-
Coupled Amplifier (CCA) [1-4]. MOS transistor mismatch often happens after fabrication until 
3%, depends on the fabrication technology [5]. There are some MOS transistor parameters 
which can be considered, such as mismatch in mobility, W/L ratio, oxide capacitance and 
threshold voltage. Furthermore, the W/L ratio corresponds to transconductance (gm) [6].  
As shown in Figure 1, biosignals, such as Electroencephalogram (EEG), 
Electrooculogram (EOG), Electrocardiogram (ECG), Electromyogram (EMG) are widely used for 
medical applications and have small amplitude and low frequency. The biosignals amplitude 
and frequency are in the order of µV to mV and DC to a few kHz, respectively [7-12].  
Common-Mode Rejection Ratio (CMRR) is ratio of differential gain and common-mode gain 
(Acm). As parameter of CMRR, Acm is important to be reduced when main circuit like CCA is 
applied for biosignals. The smaller the Acm the better the CMRR [13-15].  
 
 
Frequency (kHz)
10-4 10110-110-210-3 100
10-5
10-4
10-3
10-2
10-1
EEG
ECG
EMG
EOG
 
 
Figure 1. Voltage and frequency ranges of some biosignals 
TELKOMNIKA  ISSN: 1693-6930  
Transistor mismatch effect on common-mode gain of cross-coupled amplifier (Zainul Abidin) 
449 
Furthermore, common-mode voltage (Vcm) can be caused by power-line interference 
which normally has frequency of 50Hz or 60 Hz, depends on local power-line frequency. 
Therefore, the Vcm becomes problem for biosignal processing [16-20]. In this paper, study of gm 
mismatch effect on Acm of CCA by large signal analysis (mathematical derivation) and 
simulation is presented. Section 2 discusses the mathematical derivation of circuit analysis of 
CCA based on the effect of gm mismatch on its Acm. Section 3 describes simulation results 
representing gm mismatch effect on Acm of CCA. Finally, section 4 concludes this study. 
 
 
2. Transconductance Mismatch Effect on Cross-coupled Amplifier 
In some text books and literatures, CCA can be realized as shown in  
Figure 2 [2], [21, 22]. It consists of 2 differential pairs which matching between MOS transistors 
is very important to achieve low common-mode gain. In order to simplified the circuit analysis, 
Rs and Rd are used with well-matched condition. MOS transistor mismatch often occurs due to 
W/L ratio which is designed by circuit designer [23]. Furthermore, W/L ratio has relationship with 
gm as mentioned in (1) [24, 25]. Therefore, the effect of gm mismatch on 2 differential pairs of 
CCA is analyzed in this section. 
 
𝑔𝑚 =  
𝜕𝐼𝑑
𝜕𝑉𝑔𝑠
  
      =  √2𝜇𝐶𝑜𝑥
𝑊
𝐿
|𝐼𝑑|(1 + 𝜆𝑉𝑑𝑠) 
      =  √2𝜇𝐶𝑜𝑥
𝑊
𝐿
|𝐼𝑑| (1) 
 
Firstly, the circuit analysis is started with drain to source current (Id) definition. Based on 
large signal analysis, Id of M1-M4 in Figure 1 can be defined as 𝐼𝑑𝑖 = 𝑔𝑚𝑖𝑉𝑔𝑠𝑖| 𝑖 𝜖 {1,2,3,4}. Giving 
Vcm as the input into gates of the MOS transistors, the Id of the M1-M4 become 
 
𝐼𝑑1,2 =  𝑔𝑚1,2(𝑉𝑐𝑚 − 𝑉𝑎) (2) 
 
𝐼𝑑3,4 =  𝑔𝑚3,4(𝑉𝑐𝑚 − 𝑉𝑏) (3) 
 
 
current flows through Rs can be defined as follows: 
 
𝐼𝑑1 + 𝐼𝑑2 =  
𝑉𝑎
𝑅𝑠
 (4) 
 
𝐼𝑑3 + 𝐼𝑑4 =  
𝑉𝑏
𝑅𝑠
 (5) 
 
 
Va
M4
M1 M2
Rd
M3
Rd
RsRs
Id1 Id2 Id3 Id4
Vb
Id1+Id3 Id2+Id4
Vop
Von
 
 
Figure 2. CCA simplified with Rs and Rd 
                   ISSN: 1693-6930 
TELKOMNIKA  Vol. 17, No. 1, February 2019:  448-452 
450 
 
substituting (2–5), Va and Vb can be derived as follow: 
 
𝑉𝑎 =  
(𝑔𝑚1+𝑔𝑚2)𝑅𝑠
(𝑔𝑚1+𝑔𝑚2)𝑅𝑠+1
𝑉𝑐𝑚 (6) 
 
𝑉𝑏 =  
(𝑔𝑚3+𝑔𝑚4)𝑅𝑠
(𝑔𝑚3+𝑔𝑚4)𝑅𝑠+1
𝑉𝑐𝑚 (7) 
 
on the other hand, Vop and Von can be derived as follow: 
 
𝑉𝑜𝑝 =  −(𝐼𝑑2 + 𝐼𝑑4)𝑅𝑑  
       =  −[𝑔𝑚2(𝑉𝑐𝑚 − 𝑉𝑎) + 𝑔𝑚4(𝑉𝑐𝑚 − 𝑉𝑏)]𝑅𝑑 (8) 
 
𝑉𝑜𝑛 =  −(𝐼𝑑1 + 𝐼𝑑3)𝑅𝑑  
       =  −[𝑔𝑚1(𝑉𝑐𝑚 − 𝑉𝑎) + 𝑔𝑚3(𝑉𝑐𝑚 − 𝑉𝑏)]𝑅𝑑 (9) 
 
output voltage ( outV ) can be calculated as follows: 
 
Δ𝑉𝑜𝑢𝑡 =  𝑉𝑜𝑝 + 𝑉𝑜𝑛  
            =  [(𝑔𝑚1 +  𝑔𝑚3 − 𝑔𝑚2 − 𝑔𝑚4)𝑉𝑐𝑚 − (𝑔𝑚1 − 𝑔𝑚2)𝑉𝑎 − (𝑔𝑚3 − 𝑔𝑚4)𝑉𝑏]𝑅𝑑 (10) 
 
defining Δ𝑉𝑐𝑚 as (𝑉𝑐𝑚 + 𝑉𝑐𝑚)/2 and mismatched 𝑔𝑚𝑗 as 𝑔𝑚𝑗+1(1 + Δ𝑗+1) | 𝑗 𝜖 {1,3}, where Δ𝑗+1 is 
mismatch rate of 𝑔𝑚𝑗+1, Acm can be derived as follows. 
 
𝐴𝑐𝑚 =  
Δ𝑉𝑜𝑢𝑡
Δ𝑉𝑐𝑚
  
         = [𝑔𝑚2Δ2 + 𝑔𝑚4Δ4 −
𝑔𝑚2Δ2𝛼𝑅𝑠
𝛼𝑅𝑠+1
−
𝑔𝑚4Δ4𝛽𝑅𝑠
𝛽𝑅𝑠+1
] 𝑅𝑑  
         = [𝑔𝑚2Δ2 (1 −
𝛼𝑅𝑠
𝛼𝑅𝑠+1
) + 𝑔𝑚4Δ4 (
𝛽𝑅𝑠
𝛽𝑅𝑠+1
)] 𝑅𝑑 (11) 
 
Where 𝛼 and 𝛽 stand for 𝑔𝑚2(2 + Δ2) and 𝑔𝑚4(2 + Δ4) , respectively. From the above 
derivation, the Acm of CCA is proportional to mismatch of gm. Based on (11), the Acm is finite, so 
that some amount of Vcm may pass through the CCA. If the CCA is applied to enhanced 
amplifier, the Vcm will be amplified and deteriorate performance of the enhanced amplifier. 
 
 
3. Simulation Result 
In this section, the gm mismatch effect was evaluated using simulations. Referring  
to (11), the simulations were done based on the condition on Table 1. Well-matched resistors Rs 
and Rd were given with the value of 100 kΩ and 2 kΩ, respectively. Mismatch rate of both gm1 
and gm2 are set in the range of 0,05% - 1%. 
 
 
Table 1. Simulation Condition 
Variable Value 
Rs 100 kΩ 
Rd 2 kΩ 
∆2, ∆4 0,05% - 1% 
 
 
3.1. Effect of Increasing Mismatch Rate to Acm 
In this subsection the effect of increasing ∆ is considered and in the next subsection the 
∆ is extended to random condition. Assuming the ∆ of both gm1 and gm2 increase from 0,05% 
until 1%. Figure 3 shows simulation result based on the increasing ∆. From the simulation result, 
the Acm increases from -100 dB until -74 dB. It means the Acm increases 26 dB by the increase 
of ∆ about 1%. This means when ∆ is getting bigger, so is the Acm. 
 
TELKOMNIKA  ISSN: 1693-6930  
Transistor mismatch effect on common-mode gain of cross-coupled amplifier (Zainul Abidin) 
451 
3.2. Effect of Random Mismatch Rate to Acm 
 In order to realize the effect of random mismatch rate, Monte Carlo simulation was 
used. It was done by 500 times with random and different value of ∆2 and ∆4 to get data of Acm. 
Figure 4 shows histogram of the Acm. Because of random ∆2 and ∆4 from 0.05% until 1%, the 
Acm varies from -111.2 dB to -74.3 dB. From 500 random configuration of ∆2 and ∆4 values, most 
of Acm is in the range from -75 dB to -85 dB, therefore average Acm is -81.1 dB. The random 
mismatch rate from 0.05% until 1% increases Acm 36.9 dB. 
 
 
 
 
Figure 3. Acm [dB] based on increasing ∆ from 0.05% until 1%. 
 
 
 
 
Figure 4. Acm [dB] based on random mismatch rate from 0.05% until 1%. 
 
 
4. Conclusion 
The effect of transistor mismatch on common-mode gain of cross-coupled amplifier has 
been presented and identified based on mathematical derivation and simulation. The  
common-mode gain increases along with the increase in transconductance mismatch rate. The 
results can be used by analog circuit designer to design enhanced operational amplifier with low 
transistor mismatch effect on common-mode gain.  
In the future, mathematical derivation and simulation based on multiple mismatch of 
MOS transistor parameters such as Rs, Rd, threshold voltage, mobility, and oxide capacitance 
will be considered in order to represent actual condition. Furthermore, development of  
common-mode gain reducer and layout technique are also necessary. 
 
 
Acknowledgement 
This work is supported by Lembaga Penelitian dan Pengabdian Masyarakat Universitas 
Brawijaya (LPPM - UB) through Hibah Peneliti Pemula (Award No. 713.40/UN10.C10/PN/2018). 
 
 
References 
[1]  Younghyun Y, Hyungdong R, Jeongjin R. A True 0.4-V Delta–Sigma Modulator Using a Mixed DDA 
Integrator Without Clock Boosted Switches. IEEE Transactions on Circuits and Systems II: Express 
Briefs. 2014; 61 (4): 229-233. 
-105
-100
-95
-90
-85
-80
-75
-70
-65
-60
A
c
m
 (
d
B
) 
Mismatch rate (%)  
9 
218 
188 
60 
18 
5 2 0 0 
0
50
100
150
200
250
-70 -75 -80 -85 -90 -95 -100 -105 -110
N
u
m
b
e
r 
o
f 
S
im
u
la
ti
o
n
 
Acm [dB] 
                   ISSN: 1693-6930 
TELKOMNIKA  Vol. 17, No. 1, February 2019:  448-452 
452 
[2]  Abidin Z, Tanno K, Mago S, Tamura H. A New Instrumentation Amplifier Architecture Based on 
Differential Difference Amplifier for Biological Signal Processing. International Journal of Electrical 
and Computer Engineering. 2017; 7(2): 759-766. 
[3]  Tanaka A, Qin Z, Yoshizawa H. A 0.5-V 85-nW Rail-to-rail Operational Amplifier with a Cross-coupled 
Output Stage. 2013 IEEE 20th International Conference on Electronics, Circuits, and Systems 
(ICECS). Abu Dhabi. 2013: 137-140. 
[4]  Ghanad MA, Green MM, Dehollain C. Improving Signal to Noise of Current Mode Circuits by A Cross-
coupled Current Mirror Topology. Electronics Letters. 2014; 50 (13): 928-930. 
[5]  Chen Kaiyuan, Chatterjee T, Christensen K, Rosal J, Edwards H. Atomic Force Probing in Analog 
MOSFETs. The 31
st
 International Symposium for Testing and Failure Analysis (ISTFA). California. 
2005: 311-315. 
[6]  Hajimiri A, Heald R. Design Issues in Cross-Coupled Inverter Sense Amplifier. IEEE International 
Symposium on Circuits and Systems (ISCAS). California. 1998; 6: 311-315. 
[7]  Abidin Z, Tanno K, Mago S, Tamura H. Novel Instrumentation Amplifier Architectures Insensitive to 
Resistor Mismatches and Offset Voltage for Biological Signal Processing. The 46
th
 International 
Symposium on Multiple-Valued Logic (ISMVL). Sapporo. 2016: 194-199. 
[8]  Xiaodan Z, Xiaoyuan X, Libin Y, and Yong L. A 1-V 450-nW fully integrated programmable 
biomedical sensor interface chip. IEEE J. Solid-State Circuits. 2009; 44 (4): 1067-1077. 
[9]  Webster J. G. Medical Instrumentation: Application and Design. Third Edition. New York: Wiley. 
1998: 259. 
[10]  Chih-Jen Y, Wen-Yaw C, Mely Chen C. Micro-Power Low Offset Instrumentation Amplifier IC Design 
For Bio-Medical System Applications. IEEE Transactions On Circuits And Systems-I: Regular Papers. 
2004; 51(4): 691-699. 
[11]  Setiawidayat S, Joegijantoro R. Algorithm for the Representation of Parameter Values of 
Electrocardiogram.TELKOMNIKA Telecommunication Computing Electronics and Control. 2018; 
16(3): 1295-1302. 
[12]  Sada M, Tanno K, Shimoyama M, Abidin Z, Tamura H, Toyama T. Low Offset Voltgae 
Instrumentation Amplifier by Using Double Chopper Stabilization Technique. International 
Conference on Genetic and Evolutionary Computing. Yangon. 2015: 299-309. 
[13]  Yu CG, Geiger RL. Nonideality consideration for high-precision amplifiers-analysis of random 
common-mode rejection ratio. IEEE Transactions on Circuits and Systems I: Fundamental Theory 
and Applications. 1993; 40 (1): 1-12. 
[14]  Reza A, Edgar Sanchez-Sinencio. A biopotential amplifier with improved common mode gain. 2013 
IEEE 4th Latin American Symposium on Circuits and Systems (LASCAS). Cusco. 2013. 
[15]  Silverio AA, Chung WY, Tsai Vincent FS. A low power high CMRR CMOS instrumentation amplifier 
for Bio-impedance Spectroscopy. 2014 IEEE International Symposium on Bioelectronics and 
Bioinformatics (IEEE ISBB 2014). Chung Li. 2014: 1-4. 
[16]  Shuo W, Pengju K, Fred CL. Common Mode Noise Reduction for Boost Converters Using General 
Balance Technique. IEEE Transactions on Power Electronics. 2007; 22 (4): 1410-1416. 
[17]  Tomasini M, Benatti S, Milosevic B, Farella E, Benini L. Power Line Interference Removal for  
High-Quality Continuous Biosignal Monitoring With Low-Power Wearable Devices. IEEE Sensors 
Journal. 2016; 16 (10): 3887-3895. 
[18]  Bhateja V, Urooj S, Verma R, Mehrotra R. A Novel Approach for Suppression of Powerline 
Interference and Impulse Noise in ECG Signals. International Conference on Multimedia Signal 
Processing and Communication Technologies (IMPACT 2013). Aligarh. 2013: 103-107. 
[19]  Tashev I, Malvar H. S. Stationary-Tones Interference Cancellation using Adaptive Tracking. 2007 
IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP 2007. 
Honolulu. 2007: 201-2014. 
[20]  Ramos R, Manuel-Lazaro A, Del Rio J, Olivar G. FPGA-Based Implementation of an Adaptive 
Canceller for 50/60-Hz Interference in Electrocardiography. IEEE Transactions on Instrumentation 
and Measurement. 2007; 56 (6): 2633-2640. 
[21]  Uddin N. and Thiede A. Common Gate Cross-Coupled Differential Amplifier for Near-Field Sensors. 
Electronics Letters. 2008; 45(18): 918 – 920. 
[22]  Alzaher H and Ismail M. A CMOS fully balanced differential difference amplifier and its applications. 
IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing. 2001; 48 (6): 
614-620. 
[23]  Brito JPM. and Bampi S. A DC Offset and CMRR Analysis in a CMOS 0.35 µm Operational 
Transconductance Amplifier Using Pelgrom’s Area/Accuracy Tradeoff. Microelectronics Journal. 
2009. 40 (9): 1281-1292. 
[24]  Allen PE. and Holberg DR. CMOS Analog Circuit Design. Second Edition. New York: Oxford 
University Press. 2002: 88-89. 
[25]  Gray PR, Meyer RG. Analysis and Design of Analog Integrated Circuits. Fourth Edition. John Wiley & 
Sons, Inc. 2001: 74. 


Transistor mismatch effect on common-mode gain of cross-coupled amplifie

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