A bipolar junction transistor sitting quietly in its common-emitter configuration looks, on paper, like a nearly perfect voltage amplifier. High gain, moderate input impedance, a collector resistor that sets the operating point with textbook precision. Everything seems disciplined and predictable. Yet once the signal amplitude grows beyond the small-signal comfort zone, something shifts beneath the surface of that tidy model. The output impedance begins to breathe, pulsing in and out with every cycle. Frequencies that were never in the original signal appear at the output like uninvited guests. The transistor has not broken; it is simply doing what bipolar devices have always done. It is expressing the Early effect.
What James Early Discovered and Why It Still Matters
In the early 1950s, physicist James M. Early described a phenomenon that circuit designers had been encountering without a rigorous name for it. The Early effect is the variation in the effective width of the base in a bipolar junction transistor due to a variation in the applied base-to-collector voltage. As the collector-base junction becomes more strongly reverse-biased, its depletion region widens, encroaching into the base region itself. The neutral base, already the thinnest and most lightly doped region in the device, grows thinner still.
This geometric shift carries real electrical consequences. A narrower base means minority carriers injected from the emitter face a shorter diffusion path to the collector. The charge gradient across that shrunken base steepens and the collector current rises. If the influence of effective-base-width modulation is incorporated, the collector current characteristic is still straight but no longer flat. It carries an upward slope, indicating that output voltage affects gain: for a given V_BE, collector current will be higher if collector voltage is higher. The formal expression is the modified collector current equation: IC = IS · exp(VBE / VT) · (1 + VCE / VA), where VA is the Early voltage, the point where the family of output characteristics would theoretically converge if extrapolated into the negative voltage axis.
The Early voltage quantifies the transistor's resistance to this phenomenon. A device with VA = 200 V is far less sensitive to collector-voltage swings than one with VA = 50 V. For a modern jellybean NPN BJT such as the BC847, Early voltage comes out at roughly 100 V. In practice this means a 10 V change in VCE produces approximately a 10% change in collector current. That number sounds modest in isolation. In a high-gain amplifier stage, it is anything but.
The Output Impedance That Will Not Stand Still
In the small-signal hybrid-pi model, the Early effect is represented as a resistor ro connected between collector and emitter, in parallel with the controlled current source gm · vbe. The relationship is ro ≈ VA / IC, which reveals something important: output resistance is not a fixed property of the transistor. It depends on the quiescent collector current, and any process that shifts that current also shifts ro.
In a standard common-emitter stage, the effective output resistance is RC in parallel with ro. The Early effect limits the maximum gain possible in resistor-loaded common-emitter amplifiers by effectively acting as an additional load resistor between collector and emitter. Replace that collector resistor with a high-impedance current source, a common move in precision analog design, and ro alone governs the output impedance. Now the dependence on VCE becomes the dominant variable in the gain equation.
A small input signal sweeps VCE through a narrow range. The change in ro is modest, nearly constant over the cycle, and the distortion it introduces is low-order and well-behaved. A large input signal drives VCE through a wide arc, perhaps several volts in a single half-cycle. The output resistance ro tracks that swing in real time, dropping as VCE falls and recovering as it rises. The amplifier's output impedance is no longer a parameter; it is a signal.
From Modulated Impedance to Intermodulation Products
What happens when an amplifier stage presents a time-varying output impedance to the rest of the circuit? The collector node, instead of being a high-impedance current source that loads only weakly onto the following stage, becomes a nonlinear element that multiplies and mixes the signals passing through it. This is the mechanism that generates intermodulation distortion driven specifically by the Early effect.
The nonlinearity is not only the familiar exponential Vbe-to-Ic relationship. It is also the cyclic modulation of ro by the output voltage swing itself. The collector current equation IC = IS · exp(VBE / VT) · (1 + VCE / VA) encodes a product of two signal-dependent quantities: the exponentially controlled transconductance term and the linearly modulated base-width term. Their interaction, when VCE swings widely, produces cross-products at sum and difference frequencies.
Third-order products are particularly destructive in audio and RF applications because they fall close to the original signals in frequency, making them impossible to remove with simple filtering. A tone at f1 and a second at f2 produce intermodulation products at 2f1 - f2 and 2f2 - f1, both landing within the passband if the tones are closely spaced. The amplitude of these products scales with the cube of the input level: they rise three times faster than the fundamental in decibel terms, and the strongly nonlinear VCE-dependent term accelerates their growth compared to a device with a high Early voltage.
The cyclically modulated ro also changes how the stage interacts with its load across the signal cycle. Voltage gain Av = -gm · (ro || RC || Rload) shifts as ro shifts, meaning the positive and negative half-cycles of a large signal are amplified by slightly different gain values. This asymmetry generates even-order distortion, dominated by second-harmonic content in single-tone tests and second-order intermodulation products in two-tone tests. The stage imposes a signature on every large-amplitude waveform that passes through it.
Why the Cascode Is the Correct Answer
The diagnosis leads directly to a prescription. The cascode configuration has the first transistor operating as a common-emitter amplifier, while the second transistor operates as a common-base amplifier. The common-base stage provides a high output impedance, which helps to reduce the impact of the Early effect. The mechanism is more precise than "helps to reduce." It eliminates the root cause.
In a cascode, the lower transistor Q1 handles the input transconductance: it converts the input voltage VBE into a collector current with the familiar gain-setting relationship. The upper transistor Q2, configured as common-base, intercepts Q1's collector and presents it with a nearly fixed collector voltage. Q2's base is held at a fixed voltage, so Q1's collector is also held at a relatively fixed voltage due to Q2's VBE drop. The collector voltage of Q1 is fixed, so no Early effect can occur, and IC will remain almost constant over the full range of the supply.
This is the critical insight. The Early effect in Q1 cannot manifest because the condition that drives it, a varying VCE, has been removed. Q1's collector is clamped by Q2's emitter to a voltage that changes only by the small fraction of the output swing that couples back through Q2's finite beta. Since Q2 operates in common-base mode, its current gain is approximately unity and its input impedance looking into the emitter is only 1/gm2, which is on the order of tens of ohms. Q1 sees this low impedance as its load. A low-impedance collector load means small VCE swings at Q1's collector, regardless of how large the output voltage swings at Q2's collector.
The cascode configuration provides high intrinsic gain and high output impedance. The output resistance seen from Q2's collector is approximately gm2 · ro2 · ro1, a product that can reach hundreds of megaohms in a well-designed stage, compared to the tens or hundreds of kilohms achievable with a single transistor. Gain is therefore limited by the value of the load resistor, which the designer fully controls, not by the transistor's Early voltage.
The intermodulation picture improves for precisely the same reason. Q1's VCE is nearly constant, so its (1 + VCE / VA) term is nearly constant. The cyclic impedance modulation that sourced the intermodulation products in the simple common-emitter stage is suppressed. The high input impedance of the common-base stage helps reduce the loading effect on the common-emitter stage, contributing to enhanced linearity. In practical audio power amplifier voltage-amplification stages, cascoding the VAS transistor is one of the most reliable techniques for lowering measured THD and IMD figures, and the suppression of Early-effect-driven third-order intermodulation is a primary contributor to that improvement.
Tradeoffs and What the Designer Must Weigh
The cascode is not free of compromise. Every additional transistor consumes headroom. A cascode requires that Q2's collector-emitter junction remain out of saturation, which costs at least another VCE(sat) plus the biasing voltage at Q2's base. The practical output swing is several volts smaller than that of a single-transistor stage, a genuine constraint in low-voltage or battery-powered designs.
Biasing Q2's base demands care. A poorly bypassed bias network at Q2's base reintroduces VCE variation at Q1's collector, partially restoring the Early-effect-driven nonlinearity the topology was meant to eliminate. The bypass capacitor must present negligible impedance down to the lowest signal frequency of interest. In wide-bandwidth designs, the interaction between that bypass capacitor and the stage's internal poles can create instability that did not exist in the simpler circuit. In integrated circuits, the overhead of systematic cascoding must be weighed against the distortion targets the design must meet.
The Deeper Lesson
The common-emitter amplifier is typically analyzed as a linear, time-invariant system with a fixed small-signal model. That analysis is clean, pedagogically useful, and completely accurate for infinitesimally small signals. Real signals are never infinitesimally small, and the Early effect is a vivid demonstration of what happens when circuit parameters that appear fixed in the textbook model turn out to be functions of the very signal being amplified.
The output impedance that modulates with the collector voltage is a feedback pathway from output to transconductance that the simple hybrid-pi model does not show. It only becomes visible when the signal is large enough to drive VCE through a meaningful arc. The intermodulation products it generates grow nonlinearly with amplitude, making them disproportionately harmful at the signal levels where amplifiers are most often called upon to perform.
The cascode closes that loop by holding Q1's collector voltage constant. It transforms a parameter that was varying into one that stands still, converting a nonlinear element into something that behaves, to a much higher degree of accuracy, like the ideal controlled current source the textbook always assumed it was. Cascoding a voltage-amplification stage is not merely a matter of improving gain or bandwidth numbers. It addresses a fundamental mechanism of distortion generation, one that runs quietly in every unsuspecting common-emitter stage until the signal amplitude grows large enough to make it audible, measurable, or consequential.
Our Telegram Channel
Our YouTube Channel