Differential Pair Playground
Sweep the differential input voltage and watch current redistribute between the two transistors. Visualise Ad, Acm, CMRR, and the tail-current steering characteristic.
Diff-Pair Explorer
Differential pair (long-tailed pair)
A differential pair amplifies the difference between two inputs while rejecting signals common to both (noise, power-supply ripple). It is the input stage of every op-amp and comparator.
Common-mode rejection ratio (CMRR)
CMRR = Ad / Acm — the ratio of differential gain to common-mode gain, usually expressed in dB. Higher CMRR means better noise rejection. Practical op-amps achieve 80–120 dB. A tail current source (rather than a tail resistor) maximises CMRR by making Acm → 0.
Matching requirement
The two transistors must be closely matched — same VBE, same β — otherwise the pair has a DC offset voltage that appears as an error at the output. Monolithic IC pairs (both transistors on one die) achieve matching of a few mV; discrete pairs are much worse.
Learn more → Op-Amp Configurations — Learn
Quick experiments
- Find the linear region. Sweep the differential input near zero and the current splits almost proportionally. Push past roughly ±100 mV and the curve flattens — one transistor now carries essentially the whole tail current and the stage has stopped amplifying and started switching.
- Watch tail current set the gain. Raise Itail. Transconductance rises with it (gm = IC / VT), so differential gain rises too — at the cost of power and a narrower linear range.
- See why CMRR needs a good tail. Common-mode gain depends on the impedance of the tail source. An ideal current source gives near-zero Acm and a very high CMRR; a plain tail resistor gives a much worse figure, which is exactly why real designs spend a transistor on a current mirror there.
- Move both inputs together. Apply the same voltage to each side and the output barely moves — that rejection of the shared signal is the entire reason this topology is used for instrumentation and for op-amp front ends.
Differential pair — reference
The long-tailed pair is two matched transistors sharing one current source. That shared tail is the whole trick: the two collector currents must always sum to Itail, so whatever one transistor takes, the other gives up. The circuit responds to the difference between its inputs and largely ignores what they have in common.
Gain
At balance each device carries Itail/2, so gm = Itail / (2 VT), with VT ≈ 26 mV at room temperature. The single-ended differential gain is Ad = −gm RC, and taking the output differentially across both collectors doubles it. Gain therefore scales with bias current and load resistance, and is set by physics rather than by matching.
Common-mode rejection
Acm ≈ −RC / (2 Rtail), so CMRR = |Ad / Acm| ≈ gm Rtail. Raising the tail impedance raises rejection directly — which is why the tail is a current source, whose output impedance is hundreds of kilohms, rather than a resistor.
Why every op-amp starts this way
An op-amp is defined by amplifying V+ − V− and ignoring everything else, which is precisely what this stage does. It also gives two high-impedance inputs, a natural place to inject feedback, and — because the two devices share a die and a thermal environment — drift that largely cancels. Mismatch between the pair is what shows up on the datasheet as input offset voltage.
Where it is used besides op-amps
Comparators are the same stage run deliberately into its switching region. ECL logic uses it for very fast, low-swing gates. LVDS and CAN line receivers use it to reject the noise that a long cable picks up equally on both conductors, which is the same rejection property the sweep above demonstrates.
Common mistakes
Using a tail resistor instead of a current source.
A resistor lets tail current move with the common-mode input, which creates common-mode gain and wrecks CMRR. A current source holds it constant.
Assuming the two halves are identical.
Real transistors and resistors mismatch, producing input offset voltage. This is why op-amp input pairs are laid out adjacent and cross-coupled.
Exceeding the input common-mode range.
Drive both inputs too close to a rail and the tail current source loses headroom, collapsing the pair. The output then stops responding to the difference at all.
Expecting infinite common-mode rejection.
CMRR is finite and falls with frequency. A stage with 80 dB at DC may manage only 40 dB at 100 kHz, so high-frequency common-mode noise still gets through.
Loading one output but not the other.
Asymmetric loading converts a differential signal into a common-mode one and destroys the balance. Load both collectors equally, or take the output differentially.
Frequently asked questions
What is a differential pair used for?
It amplifies the difference between two inputs while rejecting whatever they share. That makes it the input stage of essentially every op-amp and comparator, and the reason such devices reject supply and ground noise.
What is common-mode rejection ratio?
CMRR is the ratio of differential gain to common-mode gain, usually quoted in decibels. A CMRR of 80 dB means the circuit amplifies the difference ten thousand times more than a signal common to both inputs.
Why does a differential pair need a current source in the tail?
A tail resistor lets the shared current vary with common-mode input, which produces common-mode gain. A current source holds the tail current constant, driving common-mode gain toward zero and CMRR high.
What causes input offset voltage?
Mismatch between the two transistors and their collector resistors means a small differential input is needed to make the output zero. This is why op-amp input stages use carefully matched, physically adjacent device pairs.
What is the differential gain of the pair?
For a resistively loaded pair, differential gain is gm times the collector resistance, with gm set by the tail current. Halving the tail current halves gm and therefore halves the gain.
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