Common Mode Rejection Ratio Solution

STEP 0: Pre-Calculation Summary
Formula Used
Common Mode Rejection Ratio = 20*log10(Differential Mode Gain/Common Mode Gain)
CMRR = 20*log10(Ad/Acm)
This formula uses 1 Functions, 3 Variables
Functions Used
log10 - The common logarithm, also known as the base-10 logarithm or the decimal logarithm, is a mathematical function that is the inverse of the exponential function., log10(Number)
Variables Used
Common Mode Rejection Ratio - (Measured in Decibel) - Common Mode Rejection Ratio indicates how much of the common-mode signal will appear in your measurement.
Differential Mode Gain - (Measured in Decibel) - The differential mode gain of BJT is a measure of how much the output voltage of a circuit changes in response to a differential input voltage applied to base terminals.
Common Mode Gain - (Measured in Decibel) - Common Mode Gain is typically much smaller than the differential gain. Acm is the gain given to a voltage that appears on both input terminals with respect to the ground.
STEP 1: Convert Input(s) to Base Unit
Differential Mode Gain: 105 Decibel --> 105 Decibel No Conversion Required
Common Mode Gain: 0.2 Decibel --> 0.2 Decibel No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
CMRR = 20*log10(Ad/Acm) --> 20*log10(105/0.2)
Evaluating ... ...
CMRR = 54.4031860681191
STEP 3: Convert Result to Output's Unit
54.4031860681191 Decibel --> No Conversion Required
FINAL ANSWER
54.4031860681191 54.40319 Decibel <-- Common Mode Rejection Ratio
(Calculation completed in 00.004 seconds)

Credits

Created by Prahalad Singh
Jaipur Engineering College and Research Centre (JECRC), Jaipur
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Verified by Payal Priya
Birsa Institute of Technology (BIT), Sindri
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3 Common Mode Rejection Ratio (CMRR) Calculators

Common Mode Input Resistance of BJT Half-Circuit
Go Input Resistance = (Common Emitter Current Gain*Output Resistance)*((1+(Load Resistance/(Common Emitter Current Gain*Output Resistance)))/(1+((Load Resistance+(2*Output Resistance))/Output Resistance)))
Common Mode Rejection Ratio of BJT
Go Common Mode Rejection Ratio = (2*Transconductance*Output Resistance)/(Change in Collector Resistance/Collector Resistance)
Common Mode Rejection Ratio
Go Common Mode Rejection Ratio = 20*log10(Differential Mode Gain/Common Mode Gain)

20 BJT Circuit Calculators

Transition Frequency of BJT
Go Transition Frequency = Transconductance/(2*pi*(Emitter-Base Capacitance+Collector-Base Junction Capacitance))
Base Current of PNP Transistor using Saturation Current
Go Base Current = (Saturation Current/Common Emitter Current Gain)*e^(Base-Emitter Voltage/Thermal Voltage)
Total Power Dissipated in BJT
Go Power = Collector-Emitter Voltage*Collector Current+Base-Emitter Voltage*Base Current
Unity-Gain Bandwidth of BJT
Go Unity-Gain Bandwidth = Transconductance/(Emitter-Base Capacitance+Collector-Base Junction Capacitance)
Reference Current of BJT Mirror
Go Reference Current = Collector Current+(2*Collector Current)/Common Emitter Current Gain
Common Mode Rejection Ratio
Go Common Mode Rejection Ratio = 20*log10(Differential Mode Gain/Common Mode Gain)
Output Resistance of BJT
Go Resistance = (Supply Voltage+Collector-Emitter Voltage)/Collector Current
Thermal Equilibrium Concentration of Minority Charge Carrier
Go Thermal Equilibrium Concentration = ((Intrinsic Carrier Density)^2)/Doping Concentration of Base
Output Voltage of BJT Amplifier
Go Output Voltage = Supply Voltage-Drain Current*Load Resistance
Total Power Supplied in BJT
Go Power = Supply Voltage*(Collector Current+Input Current)
Common-Base Current Gain
Go Common-Base Current Gain = Common Emitter Current Gain/(Common Emitter Current Gain+1)
Collector to Emitter Voltage at Saturation
Go Collector-Emitter Voltage = Base-Emitter Voltage-Base-Collector Voltage
Base Current of PNP Transistor given Emitter Current
Go Base Current = Emitter Current/(Common Emitter Current Gain+1)
Base Current of PNP Transistor using Collector Current
Go Base Current = Collector Current/Common Emitter Current Gain
Collector Current using Emitter Current
Go Collector Current = Common-Base Current Gain*Emitter Current
Base Current of PNP Transistor using Common-Base Current Gain
Go Base Current = (1-Common-Base Current Gain)*Emitter Current
Collector Current of BJT
Go Collector Current = Emitter Current-Base Current
Emitter Current of BJT
Go Emitter Current = Collector Current+Base Current
Short-Circuit Transconductance
Go Transconductance = Output Current/Input Voltage
Intrinsic Gain of BJT
Go Intrinsic Gain = Early Voltage/Thermal Voltage

Common Mode Rejection Ratio Formula

Common Mode Rejection Ratio = 20*log10(Differential Mode Gain/Common Mode Gain)
CMRR = 20*log10(Ad/Acm)

Differential Mode Gain

Differential Mode Gain measured in db and denoted as Ad. The gain given to a voltage that appears between the two input terminals. It represents two different voltages on the inputs.

Common Mode Gain

Common Mode Gain measured in db and denoted as Acm. The gain given to a voltage that appears on both input terminals with respect to ground. This it the same input on both terminals

How to Calculate Common Mode Rejection Ratio?

Common Mode Rejection Ratio calculator uses Common Mode Rejection Ratio = 20*log10(Differential Mode Gain/Common Mode Gain) to calculate the Common Mode Rejection Ratio, Common Mode Rejection Ratio -> The efficiency of a differential amplifier is measured by the degree of its rejection of common-mode signals in preference to differential signals. This is usually quantified by a measure known as the common-mode rejection ratio (CMRR). Common Mode Rejection Ratio is denoted by CMRR symbol.

How to calculate Common Mode Rejection Ratio using this online calculator? To use this online calculator for Common Mode Rejection Ratio, enter Differential Mode Gain (Ad) & Common Mode Gain (Acm) and hit the calculate button. Here is how the Common Mode Rejection Ratio calculation can be explained with given input values -> 54.40319 = 20*log10(105/0.2).

FAQ

What is Common Mode Rejection Ratio?
Common Mode Rejection Ratio -> The efficiency of a differential amplifier is measured by the degree of its rejection of common-mode signals in preference to differential signals. This is usually quantified by a measure known as the common-mode rejection ratio (CMRR) and is represented as CMRR = 20*log10(Ad/Acm) or Common Mode Rejection Ratio = 20*log10(Differential Mode Gain/Common Mode Gain). The differential mode gain of BJT is a measure of how much the output voltage of a circuit changes in response to a differential input voltage applied to base terminals & Common Mode Gain is typically much smaller than the differential gain. Acm is the gain given to a voltage that appears on both input terminals with respect to the ground.
How to calculate Common Mode Rejection Ratio?
Common Mode Rejection Ratio -> The efficiency of a differential amplifier is measured by the degree of its rejection of common-mode signals in preference to differential signals. This is usually quantified by a measure known as the common-mode rejection ratio (CMRR) is calculated using Common Mode Rejection Ratio = 20*log10(Differential Mode Gain/Common Mode Gain). To calculate Common Mode Rejection Ratio, you need Differential Mode Gain (Ad) & Common Mode Gain (Acm). With our tool, you need to enter the respective value for Differential Mode Gain & Common Mode Gain and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Common Mode Rejection Ratio?
In this formula, Common Mode Rejection Ratio uses Differential Mode Gain & Common Mode Gain. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Common Mode Rejection Ratio = (2*Transconductance*Output Resistance)/(Change in Collector Resistance/Collector Resistance)
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