Common-mode signal
In electronics, a common-mode signal refers to the component of an electrical signal that appears identically in both magnitude and phase across the two inputs or conductors of a differential system, typically defined as the average of the two signals: v_{cm}(t) = \frac{v_1(t) + v_2(t)}{2}.[1] This shared signal component contrasts with the differential-mode signal, which is the difference between the two: v_d(t) = v_1(t) - v_2(t).[2] Together, these modes fully describe the input signals in balanced systems, where v_1(t) = v_{cm}(t) + \frac{v_d(t)}{2} and v_2(t) = v_{cm}(t) - \frac{v_d(t)}{2}.[1] Common-mode signals often originate from external noise sources, such as electromagnetic interference (EMI), power supply variations, crosstalk, or ground potential differences, which affect both lines equally.[3] In differential amplifiers and transmission lines, the goal is to reject or suppress the common-mode component while amplifying the differential signal, a capability quantified by the common-mode rejection ratio (CMRR), defined as \text{CMRR} = 20 \log_{10} \left( \frac{A_d}{A_{cm}} \right), where A_d is the differential gain and A_{cm} is the common-mode gain.[1] High CMRR values (typically >80 dB in precision circuits) ensure that unwanted common-mode noise does not degrade signal integrity.[2] The analysis and mitigation of common-mode signals are essential in applications like operational amplifiers, balanced audio lines, high-speed digital interfaces (e.g., USB or Ethernet), and power electronics, where they help minimize electromagnetic compatibility issues and improve overall system performance.[3] Techniques such as symmetric circuit design, common-mode chokes, and proper shielding are employed to convert or attenuate these signals into differential modes or eliminate them entirely.[1]Fundamentals
Definition
In electrical engineering, a common-mode signal refers to the identical component of voltage or current that appears simultaneously and with the same polarity on both input terminals of a differential device, such as an amplifier or a balanced transmission line, relative to a common reference like ground.[4] This signal is characterized by its equal amplitude and phase on both lines, distinguishing it from signals that vary oppositely between the terminals.[5] In differential systems, the common-mode signal represents the portion that affects both inputs uniformly, often arising from environmental factors rather than the intended information-carrying content.[6] The concept of the common-mode signal originated in the late 19th century with the development of balanced transmission lines for telephony, where two-wire metallic circuits were introduced to mitigate noise from ground returns and external interference.[7] This approach gained prominence between 1890 and 1910 as telephone networks expanded, with twisted-pair configurations—first tested in 1885 and widely adopted after 1891—providing inherent balance to reduce crosstalk and inductive coupling.[7] By the mid-20th century, the term became central to analog electronics, particularly with the evolution of differential amplifiers, whose foundational patent was filed by Alan Blumlein in 1936 during the vacuum tube era.[8] A practical example occurs in twisted-pair cables used for data or voice transmission, where external electromagnetic interference, such as from nearby power lines inducing a 60 Hz hum, superimposes the same voltage on both wires relative to ground, manifesting as a common-mode signal.[9] This uniform induction highlights the signal's role in describing shared perturbations in balanced systems, in opposition to the differential-mode signal that represents the useful, opposing voltage difference between the lines.[4]Mathematical Representation
The common-mode voltage V_{cm} in a two-terminal differential system is defined as the average of the voltages at the two terminals, given by the equation V_{cm} = \frac{V_1 + V_2}{2}, where V_1 and V_2 represent the instantaneous voltages at the respective terminals relative to a common reference.[4] This formulation captures the component of the signal that appears equally and in phase on both terminals, isolating it from differential variations.[4] An analogous representation applies to currents in balanced systems, where the common-mode current I_{cm} is the average of the currents through the two paths: I_{cm} = \frac{I_1 + I_2}{2}, with I_1 and I_2 denoting the currents in each conductor.[10] This definition is particularly relevant in analyzing electromagnetic interference and filter design, where common-mode currents contribute to radiated emissions.[10] The total signal at each terminal can be decomposed into common-mode and differential-mode components. Specifically, the voltages are expressed as V_1 = V_{cm} + \frac{V_{dm}}{2}, \quad V_2 = V_{cm} - \frac{V_{dm}}{2}, where V_{dm} = V_1 - V_2 is the differential-mode voltage.[11] To derive this, start from the definitions: adding the expressions for V_1 and V_2 yields V_1 + V_2 = 2V_{cm}, confirming the average; subtracting them gives V_1 - V_2 = V_{dm}, which splits the signal into symmetric (common-mode) and antisymmetric (differential-mode) parts. Thus, the total signal encompasses both V_{total} = V_{dm} + V_{cm} in a decomposed sense, enabling separate analysis of each mode.[11] For alternating-current (AC) signals, the common-mode voltage employs phasor notation to account for phase and magnitude, represented as the vector average \vec{V}_{cm} = \frac{\vec{V_a} + \vec{V_b}}{2}, where \vec{V_a} and \vec{V_b} are the phasors of the voltages at terminals a and b.[4] This extends the time-domain average to the frequency domain, preserving in-phase equality for common-mode components in balanced lines.[4]Signal Decomposition in Differential Systems
Differential-Mode Signal
The differential-mode signal refers to the voltage or current difference between two terminals or conductors in a balanced system, representing the intended information-carrying component that conveys the primary signal content.[12] This signal arises in differential transmission schemes where the useful data is encoded in the relative variation between the two lines, rather than their absolute potentials.[13] Mathematically, the differential-mode voltage V_{dm} is extracted from the total signals on the two conductors, V_1 and V_2, through decomposition into differential and common-mode parts. In the standard convention for many electronic applications, V_{dm} = V_1 - V_2, where this difference directly captures the full signal amplitude across the pair.[14] An alternative convention, common in analyses of symmetric systems, defines V_{dm} = \frac{V_1 - V_2}{2}, which represents the effective voltage swing on each conductor relative to the pair's midpoint; this form facilitates half-circuit modeling by treating each line as carrying an equal but opposite portion of the signal.[15] The derivation stems from expressing each conductor voltage as V_1 = V_{cm} + V_{dm} and V_2 = V_{cm} - V_{dm} (or adjusted by the factor of 2), isolating the differential component by subtraction after averaging for the common-mode term.[16] In balanced systems, the differential-mode signal possesses odd symmetry, meaning the waveform on one conductor is the inverted version of the other, resulting in currents flowing in opposite directions and voltages of equal magnitude but opposite polarity.[17] This antisymmetric nature enables the signal to propagate effectively without relying on a ground reference, as the information is fully contained in the difference, minimizing susceptibility to certain imbalances.[18] A representative example occurs in balanced audio lines, where the desired audio signal manifests as opposite polarities on the two conductors—typically +V/2 on one and -V/2 on the other—allowing the receiver to recover the full voltage V by differential subtraction while rejecting external interference.[19]Common-Mode vs. Differential-Mode Comparison
In differential systems, common-mode signals and differential-mode signals represent distinct modes of voltage or current propagation across paired conductors. Common-mode signals feature even symmetry, where the voltage or current on both lines is identical in magnitude and phase relative to a common reference, such as ground.[5] In contrast, differential-mode signals exhibit odd symmetry, with voltages or currents of equal magnitude but opposite phase on the two lines, allowing the intended signal to be recovered by subtraction.[20] These symmetries align with their mathematical representations as prerequisites for understanding mode interactions in balanced systems. Typically, differential-mode carries the desired information signal, while common-mode often manifests as unwanted noise or interference.[5] A key interaction between these modes arises in unbalanced lines, where differential signals can induce common-mode components through mode conversion. This occurs due to impedance mismatches between the conductors, causing portions of the differential energy to transform into common-mode noise that propagates along the common reference path.[21] Such conversion disrupts signal integrity by introducing crosstalk, as the converted common-mode component radiates electromagnetic interference (EMI) more readily than the balanced differential mode.[20] Asymmetries in the system, such as uneven conductor lengths, dielectric variations, or mismatched grounding, exacerbate these effects by promoting further crosstalk between modes. For instance, in differential via configurations, asymmetric ground via placement can lead to significant differential-to-common-mode conversion, with noise levels varying by up to 80 dB depending on symmetry quality.[22] This imbalance not only amplifies EMI susceptibility but also reduces the overall effectiveness of differential signaling in rejecting external noise.| Property | Common-Mode Signal | Differential-Mode Signal |
|---|---|---|
| Symmetry | Even (same magnitude and phase on both lines relative to ground) | Odd (equal magnitude but opposite phase on the two lines) |
| Propagation | Currents flow in the same direction; returns via ground or earth capacitance | Currents flow in opposite directions; line-to-line measurement with field cancellation |
| Susceptibility to EMI | High; intensified fields lead to strong radiation (up to 1000x differential mode) | Low; mutual cancellation minimizes emissions and noise pickup |
| Detection Method | Measured relative to ground reference (e.g., using a current probe on the entire pair) | Obtained by subtraction of line voltages (e.g., using a differential probe) |
| Role in Systems | Often unwanted noise or bias; prone to mode conversion in imbalances | Desired signal; susceptible to conversion to common-mode due to asymmetries |