CMRR

Rev 1.09/15/13

CMRR Specification

Definitions and Equations for CMRR

CMRR(dB) = 20 Log (ΔVosi / Δ Vcm) (data sheet)

CMRR(Linear-Gain) = 10(CMRR(dB)/20) (solve for linear gain)

CMRR(Linear-Gain) = ΔVosi / Δ Vcm

Hand Calculation: Simulated results:

Vosi1 244μV:= Vosi2 259.2μV:=ΔVosi ΔVcm 10

CMR dB( )-

20

=

ΔVosi Vosi2 Vosi-= 15.2μV=

ΔVosi 12 10

120-

20

= 12μV=

Note: Vos is defined for this condition.

Vcm = Vs/2

Vs/2 = GND in this case

Note: Vos is affected by Vcm.

Vcm = Vs/2 + 12V

AC CMRR Example OPA170

Vcm = VinVcm = 0V

Vcm = Vsupply / 2

AC CMRR Example OPA170

AC CMRR Example OPA170

AC CMRR – Run Transient

AC CMRR – Transient Results

Vout1_CMR .7712209mV 1.2594- mV( )-= 2.031 mVpp=

Vout2 .5131166mV 1.48959- mV( )-= 2.003 mVpp=

AC CMRR – Simulated vs. Calculated

CMRR @ 100kHz = 45dB

Calculated Vout

ΔVosi ΔVout= 2mV 10

40- dB

20

= 20μV=

Vout Vin ΔVosi-= 2mVpp 20μV-= 1.98mVpp=

Vout Vin ΔVosi+= 2mVpp 20μV+= 2.02mVpp=

Simulated Vout

Vout1_CMR 2.031 mVpp=

-18V

+18V

R1 10k RF 10k

R3 10k R2 10k

+

-

+

U1 OPA2188

V+

Vout

+

Vcm_in

Vdif_in

-18V+18V

-18V

+18V-18V

+18V

+18V

-18V

VEE 18VCC 18

R4 10k R5 10k

R6 10k R7 10k

+

-

+

U2 OPA2188

V+

VM1

+

Vcm_in

+

-

+

U3 OPA2188

R8 10k

+

-

+

U4 OPA2188

R10 10k

R9

10k

Vin_dif 1

Common mode rejection for Dif-Amps and INAs

INA-188.TSCDif-188.TSC

Dif-Amp

CMRR 20 log10V 10- V( )-

10.92- V 6.95- V( )-

134=:= dB

• Assuming the resistors are ideal the Op-Amp CMRR is dominant• Above shows a dc sweep with ideal 10k resistors• Note: CMRR is always input referred, but in this case Gain = 1.

Relating Dif Amp CMRR with Op-amp CMRR

T

Input voltage (V)

-10.00 0.00 10.00

Vcm_opa

-5.00

5.00

Vos_opa

-7.06u

-5.08u

Vout

-10.92u

-6.95u

-18V

+18V

R1 10k RF 10k

R3 10k R2 10k

+

-

+

U1 OPA2188

V+

Vout

+

Vcm_in

V+

Vcm_opa

V+

Vos_opa

CMRR_OPA 20LogV cm_opa

V os

20 log5V 5- V( )-

7.06- V 5.08- V( )-

134.1dB

Same Circuit, Different Op-Amp

T

Input voltage (V)

-10.00 0.00 10.00

Vcm_opa

-5.00

5.00

Vos_opa

-547.93u

-518.08u

Vout

-1.10m

-1.04m

-18V

+18V

R1 10k RF 10k

R3 10k R2 10k

V+

Vout

+

Vcm_in

V+

Vcm_opa

V+

Vos_opa +

-

V+

U2 OPA1652

CMRR_OPA 20LogV cm_opa

V os

20 log5V 5- V( )-

547.9- V 518- V( )-

110.5dB

Worst Case CMRR for 0.1% ResistorsT

Input voltage (V)

-10.00 0.00 10.00

Vol

tage

(V

)

-20.03m

0.00

20.01m

CMRR_DIF 20LogV cm_opa

V os

20 log10V 10- V( )-20mV 20- mV( )-

54dB

• The output shifts 40mV (worst case) for 0.1% resistor tolerance• The output shifted 4μV for ideal resistor (limited by CMRR of Op-Amp)• 10,000x difference between ideal and practical resistors.

-18V

+18V

R1 10k RF 10k

R3 10k R2 10k

+

-

+

U1 OPA2188

V+

Vout

+

Vcm_in

Dif-188-to-OPA-CMRR.TSC

Monte Carlo Analysis CMRR 0.1% Resistors

• Monte Carlo Analysis shows expected distribution of CMRR • The majority of the population has poor CMRR (i.e. CMRR < 70dB)• Better CMRR could be achieved with tighter tolerance (i.e. 0.01%)• Worse CMRR could be achieved with looser tolerance (i.e. 1%)

ac CMRR for Ideal and Practical Resistors

-18V

+18V

R1 9.998k RF 10.003k

R3 10.002k R2 10.001k

+

-

+

U1 OPA2188

V+

Vout

+

Vcm_ac

ac-CMRR-188-DIF-AMP.TSC

Monolithic IC vs. Discrete Resistors

• Laser trim gets better accuracy then 0.1% resistors.• Resistor Drift Cancels• Tested system (i.e. CMRR, Gain, and other specifications assured)• Smaller area and lower overall cost.

Classic 3 Amp INA

opa333-discrete.TSC

Common mode Variation for 0.1% Discrete Resistors

CMRR 20logVcm_max Vcm_min-

Vout_max Vout_min-

Gain

20 log2V 2- V( )-

1.5mV 1.5- mV( )-[ ]

5

76.5dB

Note: CMRR is always referred to the input. The output shift is divided by gain, so CMRR normally improves at higher gains.

opa333-discrete-cmrr.TSC

Special Topology – PGA280/281