Concept

Miller effect — where it appears

The apparent multiplication of a capacitance between an inverting stage's input and output by one plus the stage's gain, seen from the input. It is why a few picofarads from collector to base can set a whole amplifier stage's bandwidth.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

A common-emitter stage with 2.0 pF from collector to base. computed by solving, not by drawing. The stage's midband gain is 144.7 and its −3 dB point is at 504 kHz. The Miller approximation lumps 311 pF at the input and predicts 643 kHz — 21.6% high. The network's second pole is at 336 MHz and its right-half-plane zero at 3.08 GHz, both of which the approximation has no room for.

The frequency a device sets for itself

A common-emitter stage's bandwidth is decided by two picofarads between its collector and its base. The Miller approximation says how — lump it at the input, multiplied by one plus the gain — and predicts 643 kHz where the solved network gives 504 kHz. Twenty-two per cent optimistic, and it has no room at all for the second pole or for the zero in the right half-plane that the network also has.

semiconductors · Device bandwidth

The common-emitter stage from a 100 Ω source: the solved response against the Miller estimate. computed by solving, not by drawing. The stage of 1 mA, 5 kΩ load, Cπ 20 pF and Cμ 2 pF has a gain from base to collector of 182.0. From 100 Ω the network's bandwidth is 3.41 MHz; the Miller estimate — Cμ moved to the input, multiplied by one plus the gain — says 4.23 MHz, 1.24 times it. The estimate has one pole, at the input; the network has two, and from a low source the second is the one that sets the bandwidth.

The node the bandwidth belongs to

The Miller estimate puts a common-emitter stage's bandwidth at its input node, and whether that is right depends on the source. From 10 kΩ it is within 1% at every load from a gain of 19 to 1,190; from 100 Ω it is 24% optimistic and from 10 Ω 3.41 times, because the input node has become fast and the output node sets the bandwidth. The stage's two poles split from 92 to 2,993 times apart as the source rises. A load capacitance the estimate cannot see takes the bandwidth from 12.1 MHz to 1.49 MHz from 10 Ω and moves it 6% from 100 kΩ. And the multiplier is the gain from base to collector, 182 — not the 144.7 from the source.

semiconductors · Device bandwidth

A cascode is 15.9 times wider than the plain stage from 100 kΩ and 1.30 times from 10 Ω, with a 5 kΩ load. computed by solving, not by drawing, each bandwidth bisected on the solved magnitude. The common-emitter stage of 1 mA, Cπ 20 pF and Cμ 2 pF into 5 kΩ, alone and with a second device stacked on its collector, across four decades of source resistance. The plain stage falls from 12.1 MHz to 110 kHz as its Miller-multiplied input node slows. The cascode runs from 15.8 MHz, where its output node sets the bandwidth — Cμ2 against 5 kΩ, 15.9 MHz — to 1.75 MHz, where its input node does: rπ in parallel with the source, against Cπ and twice Cμ, 1.78 MHz. Neither single-node figure is ever below the stage's own bandwidth. The faint line is the cascode with the upper device's own Cπ left out of the middle node, and it is never below the solid one and at most 0.74% above it.

The nodes a cascode hands the bandwidth to

A cascode is said to remove the Miller effect, and into 5 kΩ it does: from a 100 kΩ source it is 15.9 times wider than the plain stage. From 10 Ω it is 1.30 times wider, because there the bandwidth was never the input's — it belongs to the output node, Cμ2 against the load, 10.0 ns from every source. From a high source it belongs to the input, which is now rπ against Cπ and twice Cμ rather than against a multiplied Cμ, 74.7 ns of Cπ beside 15.4 of Cμ. The node the cascode adds holds 0.545 ns and moves the bandwidth less than one per cent. Its three poles cross rather than split, the sum of time constants is worst — 24% low — at the source where two nodes are equally slow, and the removal is not unconditional: the middle node's gain is 1.01 at a 1 kΩ load, 12.3 at 1 MΩ, and above 3.11 MΩ the cascode is narrower than the stage it replaced.

semiconductors · Device bandwidth

Named alongside it

The objects these essays reach for when they reach for this one.

Bandwidth Dominant pole Input capacitance Open circuit time constants Poles Source impedance Capacitive load Cascode Gain–bandwidth product Model range Output impedance Right half-plane zero

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