Common-Mode Rejection Ratio (CMRR) is the ratio of an op-amp's differential gain to its common-mode gain. In Electrical Circuits and Systems II, it tells you how well the amplifier boosts the wanted signal while ignoring noise on both inputs.
Common-Mode Rejection Ratio, or CMRR, is the number that tells you how well an operational amplifier separates the signal you want from the signal that shows up on both inputs. In this course, that usually means comparing the differential input signal to common noise, then seeing how much less the op-amp amplifies that noise.
The basic idea is simple: an ideal op-amp amplifies only the difference between its inverting and non-inverting inputs. Real op-amps are not perfect, so some of the same signal that appears on both inputs still gets through. CMRR measures how small that unwanted common-mode response is compared with the desired differential response.
Mathematically, CMRR is the ratio of differential gain to common-mode gain, written as CMRR = Ad / Ac. A larger ratio means the op-amp is better at ignoring signals that are common to both inputs. Since the numbers can get very large, engineers usually express CMRR in decibels: CMRR(dB) = 20 log10(CMRR).
A quick way to read it is this: high CMRR is good when you are dealing with sensors, long wires, or noisy environments. For example, if both input leads pick up the same hum from nearby power lines, a high-CMRR op-amp mostly rejects that hum and keeps the differential signal.
You will also see why the number is not infinite in real life. Input transistor mismatch, temperature changes, and power supply variation can all reduce common-mode rejection. So in this course, CMRR is not just a label, it is a practical way to judge whether an op-amp circuit will behave cleanly once it leaves the idealized diagram.
CMRR shows up anywhere an op-amp is expected to work with small signals in a noisy circuit. In Electrical Circuits and Systems II, that connects directly to operational amplifier fundamentals, because ideal op-amp rules only go so far before real device limits start affecting your results.
This term matters most when you analyze whether a circuit will actually amplify the information you care about. If both inputs of an op-amp pick up the same interference, a high CMRR means that interference barely changes the output. That is why CMRR is a big deal in instrumentation-style circuits, sensor interfaces, and other setups where the useful signal may be tiny compared with the noise.
It also gives you a more realistic view of op-amp behavior. A circuit might look perfect under ideal assumptions, but poor CMRR can explain why the output still has hum, drift, or unexpected offset. That makes this term useful when you are comparing op-amp models, checking datasheets, or explaining why one design performs better than another.
CMRR connects the math to the hardware. You are not just memorizing a spec, you are learning how device mismatch and imperfect gain shape the output of real amplifier circuits.
Keep studying Electrical Circuits and Systems II Unit 9
Visual cheatsheet
view galleryDifferential Amplifier
CMRR is built around the idea of differential amplification. A differential amplifier is supposed to respond to the voltage difference between two inputs, not to signals that are the same on both inputs. If the circuit is well matched, its common-mode gain stays low and its CMRR stays high. That makes this a natural place to study why op-amp input stages are designed the way they are.
negative feedback
Negative feedback does not create CMRR by itself, but it helps shape how an op-amp circuit behaves in practice. By forcing the amplifier to correct its output, feedback can stabilize the differential response and make the circuit act closer to its intended gain. If the op-amp has weak CMRR, though, feedback cannot completely remove the effect of common-mode noise.
Input Impedance
Input impedance matters because it affects how much the op-amp loads the source and how much external noise gets coupled into the inputs. High input impedance lets the amplifier sense a signal without drawing much current from the previous stage. In noisy sensor circuits, that helps preserve the input conditions that CMRR is supposed to protect.
Voltage Gain
CMRR compares two kinds of gain: differential gain and common-mode gain. That makes voltage gain the main measurement behind the spec. When you work problems, you may calculate or compare gain values to see whether the op-amp is amplifying the desired input much more strongly than any shared noise.
A quiz or problem-set question may give you an op-amp with a differential gain and a common-mode gain and ask you to compute CMRR or CMRR in dB. You may also be asked to interpret what a large or small value means for circuit performance. In lab work, you might compare outputs with noise on both inputs and explain why one op-amp rejects that noise better than another. If the problem shows a sensor circuit or differential input stage, CMRR is the clue that tells you whether common noise should cancel or leak into the output.
A differential amplifier is the circuit behavior or topology, while CMRR is a performance metric for how well that circuit rejects common-mode signals. You can have a differential amplifier with weak CMRR if its components are poorly matched. So the amplifier is the thing, and CMRR is the number that describes how well it does its job.
Common-Mode Rejection Ratio tells you how well an op-amp rejects signals that appear equally on both inputs.
The ratio is CMRR = Ad / Ac, so bigger numbers mean better rejection of common-mode noise.
Engineers usually write CMRR in decibels because real op-amps can have very large values.
High CMRR matters most in noisy circuits, especially when the useful signal is small.
If an output still shows hum or interference, low CMRR is one possible reason.
It is a measure of how well an op-amp amplifies the difference between its inputs while ignoring signals that are the same on both inputs. In this course, it is one of the main real-world limits that separates ideal op-amp behavior from actual circuit behavior.
Use CMRR = Ad / Ac, where Ad is differential gain and Ac is common-mode gain. If you need the decibel form, use CMRR(dB) = 20 log10(CMRR). A larger dB value means better rejection of common-mode signals.
High CMRR is good because it means the op-amp is better at ignoring noise or interference that affects both inputs equally. That is especially useful in sensor circuits and other low-level signal applications. A low CMRR can leave unwanted hum or drift at the output.
Differential gain is how strongly the op-amp amplifies the difference between the two inputs. CMRR compares that desired gain to the unwanted gain from common-mode signals. So differential gain is one part of the ratio, and CMRR tells you how dominant it is.