Differential signal pair ($V_d=V_{+}-V_{-}$)

A differential signal pair carries information in the electric potential difference between two conductors. For conductor potentials $V_{+}$ and $V_{-}$ relative to a stated reference, define the differential and common-mode voltage components byEquivalently $V_{+}=V_c+V_d/2$ and $V_{-}=V_c-V_d/2$. A signal pair need not have zero common component; the receiver uses the difference while tolerating a specified range of common input potentials.^[ref]

Equal added disturbances cancel in the ideal subtraction: replacing both potentials by $V_{\pm }+n$ leaves $V_d$ unchanged. For example, inputs at $1.8$ and $1.2$ volts have $V_d=0.6$ volts. Adding $0.2$ volts to each changes $V_c$ but preserves the difference.

Real receivers have finite common-mode rejection ratio, and unequal coupling or mismatched impedances can convert a common disturbance into a differential one. Thus differential signalling is a system property involving the source, both paths and the receiver. An original test applies the same disturbance to both inputs and compares the output with a deliberately unbalanced path; it separates ideal cancellation from sensitivity to mismatch.

The common-mode rejection ratio compares a receiver's differential gain $A_d$ with its gain $A_c$ for common-mode voltage. In a linear small-signal model,A high value means that equal disturbances on the two inputs have relatively little effect on the output. It does not specify the maximum common input range before saturation.^[ref]

For $A_d=100$ and CMRR $=80$ dB, the ratio is $10000$ and $|A_c|=0.01$. A 1 V common disturbance then creates 10 mV of output error, equivalent to 0.1 mV at the differential input. A measurement applies equal input changes while keeping their difference fixed, subtracts the initial output, and compares the measured common gain with a separate differential-gain measurement. Both gains depend on frequency, so a DC specification alone does not describe rejection of a rapidly changing disturbance.

For a differential signal pair, the common-mode voltage is the average potential of the two conductors relative to a specified local reference:It is the component shared by both inputs. With $V_{+}=2.6$ V and $V_{-}=2.4$ V, the common component is 2.5 V and the differential component is 0.2 V. A 1 V change of the receiver's reference changes both measured conductor potentials equally and therefore changes $V_c$, while leaving $V_d$ unchanged.^[ref]

This decomposition is useful when a small sensor difference sits on a large shared offset. Even a receiver with excellent common-mode rejection ratio has a finite permitted common input range. A practical test therefore varies the average input while holding the difference fixed and checks when the output stops following its differential-gain calibration.