CMRR of Differential Amplifier Calculator

Estimate common mode rejection with clear gain inputs. Review ratios, decibels, and signal balance quickly. Export results for careful differential amplifier design checks today.

Calculator

Formula Used

CMRR ratio = |Ad / Acm|

CMRR dB = 20 log10(CMRR ratio)

Ad = Vout differential / Vid

Acm = Vout common mode / Vcm

Output error = |Acm × operating common mode voltage|

The calculator uses absolute gain values. This avoids sign confusion when an amplifier inverts one measured signal.

How to Use This Calculator

Select direct gain ratio when Ad and Acm are already known.

Select voltage test method when you have test input and output readings.

Enter the operating common mode voltage to estimate output error.

Add a target dB value to check if the design meets your goal.

Press Calculate. The result appears above the form.

Use Download CSV or Download PDF to save the result.

Example Data Table

Case Ad Acm CMRR Ratio CMRR dB Comment
Instrumentation input 1000 0.01 100000 100 dB Precision grade
General amplifier 500 0.05 10000 80 dB Good rejection
Weak matching 100 0.1 1000 60 dB Moderate rejection

CMRR in Differential Amplifiers

A differential amplifier should amplify the difference between two inputs. It should also reject signals that appear equally on both inputs. That rejected signal is called common mode signal. Common mode rejection ratio shows how well this rejection works.

Why CMRR Matters

High CMRR helps remove hum, sensor cable pickup, ground shift, and supply noise. It is important in instrumentation circuits, bridge sensors, audio front ends, and data converters. A low value can turn unwanted common noise into output error. This error may hide small differential signals.

Gain Based Evaluation

The basic method divides differential gain by common mode gain. Differential gain is the wanted gain. Common mode gain is the unwanted gain. The ratio is usually converted to decibels. A higher decibel value means better rejection. For example, a ratio of 10,000 equals 80 dB.

Voltage Test Method

A practical test can use measured voltages. First, apply a known differential input and measure the output. That gives differential gain. Then apply the same signal to both inputs. Measure the remaining output. That gives common mode gain. The calculator can process those test values directly.

Design Interpretation

CMRR is affected by resistor matching, device balance, input impedance, layout, and frequency. Precision resistor networks usually improve performance. Long traces and unequal source impedances can reduce real rejection. The value may also change at higher frequency. So a bench result should mention test frequency and input level.

Using the Result

Use the ratio for quick comparison. Use the decibel value for reports and datasheets. Check output error when the common mode signal is large. This helps decide whether filtering, shielding, trimming, or a better amplifier is needed. Always compare the result with the required signal accuracy. This makes the design margin easier to judge.

Good Measurement Practice

Use stable sources and accurate meters. Keep leads short during sensitive tests. Record both input and output units. Avoid saturating the amplifier during either test. Repeat the measurement at the operating frequency. If the common mode output is near zero, instrument resolution matters. In that case, report a minimum CMRR value rather than a false exact number. This keeps results honest and useful during design review and troubleshooting later work.

FAQs

What is CMRR?

CMRR means common mode rejection ratio. It compares wanted differential gain with unwanted common mode gain. Higher values show better rejection of shared noise on both inputs.

Why is CMRR shown in decibels?

Decibels make large ratios easier to read. A gain ratio may be thousands or millions. The dB value gives a compact engineering comparison.

What is a good CMRR value?

It depends on the circuit. Around 80 dB is good for many uses. Precision measurement systems may need 100 dB or higher.

Can common mode gain be zero?

In theory, yes. Then CMRR becomes infinite. In real circuits, measurement limits and imbalance usually create a very small common mode gain.

Does CMRR change with frequency?

Yes. Many amplifiers reject common mode signals less effectively at higher frequencies. Always check the operating frequency when comparing results.

Why use absolute values?

Gain polarity may be negative because of inversion. CMRR describes rejection magnitude, so absolute values give the practical rejection ratio.

What causes poor CMRR?

Poor resistor matching, unequal input impedance, layout imbalance, source mismatch, and device limits can reduce CMRR. Frequency can also reduce performance.

Can this calculator estimate output error?

Yes. Enter operating common mode voltage. The calculator multiplies it by common mode gain to estimate common mode output error.

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