Circuit Response
every model has an edge, and the figure carries it
Devices, and the amplitude they stop being linear at

The buffer that is not a buffer

An emitter follower is reached for when something has to be driven without being loaded: unity gain in, high impedance seen, low impedance presented. The last of those is a number with a range, and the range is narrow. At a kilohm of source the emitter presents 19.08 ohms at low frequency and 67 ohms at 29 megahertz, because the current gain that made it small is falling — and the peak is worst in the middle of the slider, so it cannot be avoided by making the source stiffer or softer.
16 min read 7 figures Every model has an edgeThe parasitic is the componentTwo routes to a number

Assumes: How small is small signal · A bias point is a solution, not a choice

The emitter follower is the stage that gets added at the end. Something needs driving, the thing in front of it cannot drive it, and a follower goes in between: gain of one, high input impedance, low output impedance, done.

Two of those three are approximately true and one of them has a range. The gain is 0.98 rather than 1, which nobody minds. The input impedance is high, and falls with frequency, which the field’s Miller essay is about. The output impedance is the interesting one, because it is small in exactly the way that stops being true where it matters.

A follower's output impedance from 1 kΩ of source, bare and with 100 pF on itcomputed by solving, not by drawing, on a small-signal follower at 2.0 mA with β = 150 and fT = 560 MHz. At 100 Hz the emitter presents 19.08 Ω against a textbook 1/gₘ + Rₛ/(β+1) of 19.55 Ω — the expression is an upper bound here and at every source resistance on the slider, 2.4% high at this one. What it cannot describe is the frequency axis: the β that divided the source resistance down is itself falling, so the impedance rises, and the reactance at 3 MHz is 4.3 Ω — an inductance of 0.229 µH against Rₛ/ωT = 0.284 µH. With 100 pF hung on the output that impedance peaks at 67.0 Ω at 29.3 MHz, 3.51 times its own low-frequency value: an inductive source and a capacitive load are a resonant circuit, and this one is inside a part whose output impedance is quoted as a single number.1101001k10k100k10k100k1M10M100M1Gfrequency (hertz)impedance looking into the emitter (ohms)19.1 Ω at low frequency1/gₘ + Rₛ/(β+1) = 19.5 Ωdoubled by 21.5 MHzwith 100 pF: 67 Ωsource resistance1 kΩsolved, at 100 Hz19.082 Ω1/gₘ + Rₛ/(β+1)19.549 Ωvoltage gain0.98044reactance at 3 MHz4.31 Ωas an inductance0.229 µHRₛ/ωT for comparison0.284 µHdoubles above21.5 MHzpeak with 100 pF67.0 Ω at 29.3 MHzsolved, then checked — an impedance driven one ampere at a time3.5× its own low-frequency value at 29.3 MHz
Fig. 1 The impedance looking into the emitter of a follower biased at two milliamps, driven from a kilohm, with and without a hundred picofarads of load. The lower curve is bare and the upper one is loaded; the panel carries the textbook expression beside the solved value and the reactance measured at three megahertz.

The expression, and which way it is wrong

The textbook output impedance of a follower is

Zout=1gm+Rsβ+1Z_{\mathrm{out}} = \frac{1}{g_m} + \frac{R_s}{\beta + 1}

— the source resistance divided down by the current gain, in series with the emitter’s own resistance. At two milliamps, 1/gm1/g_m is 12.93 ohms, and with a kilohm of source and a beta of 150 the second term adds 6.62, for 19.55 ohms.

The solved network gives 19.08. Which is close, and the direction is worth having: the expression is an upper bound at every source resistance on the slider, and it stays within two and a half per cent up to a kilohm.

source resistance solved expression over by
10 Ω 12.74 Ω 12.99 Ω 2.0%
100 Ω 13.32 Ω 13.59 Ω 2.0%
330 Ω 14.80 Ω 15.11 Ω 2.1%
1 kΩ 19.08 Ω 19.55 Ω 2.4%
3.3 kΩ 33.50 Ω 34.79 Ω 3.7%
10 kΩ 73.14 Ω 79.15 Ω 7.6%
100 kΩ 399.0 Ω 675.2 Ω 41%

The departure at the top of the range has a cause worth naming: once the source resistance is far above rπr_\pi — 1939 ohms here — the base is no longer being driven from anything the expression’s divider describes, and the emitter resistor and the collector resistance start to set the answer instead. Forty-one per cent is a large error, and it is conservative, which is the least dangerous kind.

A diode fed from 5 V through 1.0 kΩ. computed by solving, not by drawing. The operating point is where the exponential meets the load line: 0.692544 V and 4.3075 mA, reached in 13 damped Newton steps from a cold start. The one-line Newton on Vs = v + R·i(v), which touches no matrix, gives 0.692544 V. The "drop" is not a constant: it moves 59.53 mV per decade of current, measured between two solved operating points.
Fig. 2 Where the 12.93 ohms comes from. The transconductance is the bias current over the thermal voltage, so the emitter’s own resistance is a property of the operating point rather than of the device — and the operating point is solved by Newton on the netlist rather than chosen.

The part the expression cannot say anything about

Neither term in that expression has a frequency in it, and the impedance has one.

The division by β+1\beta + 1 is a division by a current gain, and a current gain falls above the transistor’s own beta corner. So the second term grows with frequency, and the impedance grows with it. Measured at three megahertz on the network above, the reactance is +4.31 ohms, which is positive: the emitter of a follower looks like an inductor.

Reading that reactance as an inductance gives 0.229 µH, against a rough closed form of Rs/ωTR_s/\omega_T = 0.284 µH — right in form and about twenty per cent out in constant, consistently across the slider:

source resistance measured inductance Rₛ/ωT
100 Ω 0.0215 µH 0.0284 µH
330 Ω 0.0770 µH 0.0938 µH
1 kΩ 0.229 µH 0.284 µH
3.3 kΩ 0.635 µH 0.938 µH
10 kΩ 0.899 µH 2.844 µH

At ten ohms of source there is no inductance to speak of — the reactance is slightly negative — and at a hundred kilohms it is negative again, because by then the base is driven from so high an impedance that the collector-base capacitance dominates what the emitter sees. The inductive behaviour is a middle-of-the-range phenomenon, and that turns out to matter.

A follower's output impedance from 10 Ω of source, bare and with 100 pF on it. computed by solving, not by drawing, on a small-signal follower at 2.0 mA with β = 150 and fT = 560 MHz. At 100 Hz the emitter presents 12.74 Ω against a textbook 1/gₘ + Rₛ/(β+1) of 12.99 Ω — the expression is an upper bound here and at every source resistance on the slider, 2.0% high at this one. What it cannot describe is the frequency axis: the β that divided the source resistance down is itself falling, so the impedance rises, and the reactance at 3 MHz is -0.0 Ω — capacitive rather than inductive, which is what happens once the source resistance is far above rπ. With 100 pF hung on the output that impedance peaks at 12.7 Ω at 10.0 kHz, 1.00 times its own low-frequency value: an inductive source and a capacitive load are a resonant circuit, and this one is inside a part whose output impedance is quoted as a single number.
Fig. 3 Ten ohms of source, where the impedance is 12.74 Ω and flat: no current gain is being relied on, so there is nothing for its fall to spoil. This is what a follower driven from another follower looks like, and it is the case the data sheet number describes.
A follower's output impedance from 100 kΩ of source, bare and with 100 pF on it. computed by solving, not by drawing, on a small-signal follower at 2.0 mA with β = 150 and fT = 560 MHz. At 100 Hz the emitter presents 399.00 Ω against a textbook 1/gₘ + Rₛ/(β+1) of 675.18 Ω — the expression is an upper bound here and at every source resistance on the slider, 40.9% high at this one. What it cannot describe is the frequency axis: the β that divided the source resistance down is itself falling, so the impedance rises, and the reactance at 3 MHz is -94.3 Ω — capacitive rather than inductive, which is what happens once the source resistance is far above rπ. With 100 pF hung on the output that impedance peaks at 399.0 Ω at 10.0 kHz, 1.00 times its own low-frequency value: an inductive source and a capacitive load are a resonant circuit, and this one is inside a part whose output impedance is quoted as a single number.
Fig. 4 And a hundred kilohms, where the expression is 41% high and the reactance has gone capacitive. Both ends of the slider are well behaved for opposite reasons, which is what leaves the trouble in the middle.

An inductive source and a capacitive load

An inductance and a capacitance make a resonance, and the damping is whatever resistance is in the loop. The follower supplies the inductance; anything hung on the output supplies the capacitance.

With a hundred picofarads on the emitter:

source resistance impedance at low frequency peak ratio at
10 Ω 12.74 Ω 12.7 Ω 1.00 —
100 Ω 13.32 Ω 20.3 Ω 1.52 82.5 MHz
330 Ω 14.80 Ω 41.0 Ω 2.77 48 MHz
1 kΩ 19.08 Ω 67.0 Ω 3.51 29.3 MHz
3.3 kΩ 33.50 Ω 88.2 Ω 2.63 16 MHz
10 kΩ 73.14 Ω 101.5 Ω 1.39 8.25 MHz
100 kΩ 399.0 Ω 399.0 Ω 1.00 —

The ratio column is the one to read. It rises to 3.51 at a kilohm and falls away on both sides, because at ten ohms there is no inductance and at a hundred kilohms there is none either. The worst case is in the interior of the range, which means the failure cannot be designed around by pushing the source impedance one way or the other — the usual first instinct, and here it is as likely to make things worse as better.

A stage whose data sheet says “output impedance 20 Ω” presenting 67 Ω at 29 MHz is not a small discrepancy. It is a resonance, and everything a resonance does — peaking, ringing on edges, a phase that swings through ninety degrees — comes with it.

A follower's output impedance from 10 kΩ of source, bare and with 100 pF on it. computed by solving, not by drawing, on a small-signal follower at 2.0 mA with β = 150 and fT = 560 MHz. At 100 Hz the emitter presents 73.14 Ω against a textbook 1/gₘ + Rₛ/(β+1) of 79.15 Ω — the expression is an upper bound here and at every source resistance on the slider, 7.6% high at this one. What it cannot describe is the frequency axis: the β that divided the source resistance down is itself falling, so the impedance rises, and the reactance at 3 MHz is 16.9 Ω — an inductance of 0.899 µH against Rₛ/ωT = 2.84 µH. With 100 pF hung on the output that impedance peaks at 101.5 Ω at 7.94 MHz, 1.39 times its own low-frequency value: an inductive source and a capacitive load are a resonant circuit, and this one is inside a part whose output impedance is quoted as a single number.
Fig. 5 Ten kilohms of source, where the low-frequency impedance is already 73 Ω and the peak is only 39% above it. The peaking has almost gone, and it has gone by making the flat part worse, which is not a repair.

Why the impedance rises, in words

The mechanism deserves a sentence that is not an equation, because it explains why the rise is inductive rather than merely large.

At the emitter, the follower opposes a change in voltage by changing its base-emitter voltage, which changes its collector current, which is delivered back to the emitter. That is a feedback loop, and the gain in it is the current gain of the transistor as seen from the source: how much base current the source can supply for a given disturbance, multiplied by beta.

Above the beta corner, the current gain falls at twenty decibels per decade. So the loop that was holding the emitter stiff loses gain at twenty decibels per decade, and the impedance it fails to suppress rises at twenty decibels per decade. A resistance rising in proportion to frequency is an inductive reactance — that is what the phase measurement is saying, and it is why the equivalent inductance comes out proportional to the source resistance and inversely proportional to the transit frequency.

The same sentence read backwards gives the design rule: the inductance is Rs/ωTR_s/\omega_T, so it is reduced by driving the base from a lower impedance or by using a faster transistor, and by nothing else. Increasing the bias current lowers 1/gm1/g_m and leaves the inductance alone, which is why a follower that is “not stiff enough” does not improve when it is run harder.

What a hundred picofarads is

The load in the table is a hundred picofarads, and the number was not chosen to be dramatic.

A short length of coaxial cable is about a hundred picofarads per metre. An oscilloscope probe is ten to fifteen. A length of ribbon cable to another board is more than either. The input capacitance of the next stage — a common-emitter’s Miller capacitance, for instance — is 311 pF for the stage this field measures.

So the loaded curve in the figure is not an abuse of the stage; it is the stage doing its job. A follower is put there because something capacitive has to be driven, which is precisely the condition under which its own inductance resonates.

Where this goes all the way to oscillation

The figure stops at peaking, and it is worth saying what is on the other side of it, because the follower’s reputation for oscillating is deserved and this is the mechanism.

The same analysis run from the input side gives a follower with a capacitive load an input impedance with a negative real part over a band. A negative resistance driven from an inductive source — a length of wire, a wound resistor, the output of another follower — is an oscillator, and the frequency is wherever the loop’s reactances cancel.

That case needs an inductance in the base lead to complete, which this figure does not have, so it is named rather than drawn: what is measured here is the resonance in the output impedance, which is the same reactances at a lower loop gain. The standard repairs are the same for both — a small resistor in the base, a small resistor in the emitter, or a ferrite bead — and all three work by putting loss in the loop that the transistor’s negative resistance has to overcome.

An inverting unity gain driving 2.2 nF, and the pole that is inside the loop. computed by solving, not by drawing. Two ten-kilohm resistors around a 10 MHz amplifier make a gain of 1.00, and a loop that closes against 2.01 — one plus the ratio, not the ratio. Hanging 2.2 nF on the output leaves the closed-loop gain at a kilohertz unchanged — 0.99998002 against 0.99997988 — and takes the phase margin from 90.0° to 30.1°. The mechanism is at the other end of the amplifier from the summing-junction case and the arithmetic is the same: the load works against the amplifier's own fifty ohms of output resistance, which puts a second pole in the forward path — inside the loop, where the feedback has to live with it — while the gain the loop closes against does not move at all. Forty-five degrees is reached at 905 pF, bisected on the netlist. The capacitance is not part of the signal path and does not appear in any expression for the gain.
Fig. 6 The feedback field’s version of the same problem: a capacitance on an amplifier’s output works against the output resistance to make a pole inside the loop, and ninety degrees of margin becomes thirty. Different mechanism, same component, same repair — a resistor between the output and the load.

What a follower is actually for

Given all of that, it is worth restating what the stage buys, because it does buy something.

It transforms impedance by the current gain. A kilohm of source becomes about nineteen ohms at the emitter, and a kilohm of load becomes about 150 kΩ at the base. That is a factor of fifty in each direction, and no passive network does it.

It has no Miller multiplication. The collector is at signal ground and the base-emitter voltage barely moves, so neither internal capacitance is multiplied by a gain. That is why a follower’s bandwidth is high and why it is used in front of stages that do have the problem.

It costs a diode drop and a per cent of gain. The gain here is 0.98044, and the two per cent is 1/(1+gmRE)1/(1 + g_m R_E) — the same expression that appears in the degeneration essay, doing the same job in a different place.

What it does not buy is a low impedance at all frequencies, and that is the whole content of this page.

A follower's output impedance from 3.3 kΩ of source, bare and with 100 pF on it. computed by solving, not by drawing, on a small-signal follower at 2.0 mA with β = 150 and fT = 560 MHz. At 100 Hz the emitter presents 33.50 Ω against a textbook 1/gₘ + Rₛ/(β+1) of 34.78 Ω — the expression is an upper bound here and at every source resistance on the slider, 3.7% high at this one. What it cannot describe is the frequency axis: the β that divided the source resistance down is itself falling, so the impedance rises, and the reactance at 3 MHz is 12.0 Ω — an inductance of 0.635 µH against Rₛ/ωT = 0.938 µH. With 100 pF hung on the output that impedance peaks at 87.9 Ω at 15.8 MHz, 2.62 times its own low-frequency value: an inductive source and a capacitive load are a resonant circuit, and this one is inside a part whose output impedance is quoted as a single number.
Fig. 7 A source of three and a third kilohms. The output impedance is 33.50 Ω at low frequency, its inductive part is 0.635 µH, and with a hundred picofarads hung on it the impedance peaks at 88 Ω. Read against the ten-ohm and hundred-kilohm cases above, the low-frequency figure barely moves while the peak follows the source resistance almost proportionally — because the peak is set by the inductive part and that is what β divides the source into. What a follower gives back is not a resistance; it is a resistance and an inductance, and only one of them is in the specification.

The same argument in three other places in this collection

The pattern — a quantity that is small because it is divided by a gain, and stops being small where the gain falls — is one of the most reliable in the subject.

A virtual earth is at ground because the loop holds it there, so its impedance is 0.10 Ω at direct current, rises a decade per decade, and settles at the feedback resistors in parallel with the amplifier contributing nothing.

A regulator’s output impedance is low because the loop makes it low, so it rises through the audio band and the capacitor takes over above it.

A probe’s input impedance is a megohm at direct current and a few picofarads’ worth above the compensation corner, which is why an instrument that loads nothing at all can load a circuit heavily at ten megahertz.

Each of them is the same sentence with a different denominator, and in each the useful number is not the low-frequency one but the frequency at which the division stops working.

The measurement, and why it is a current

The impedance in every figure here is measured by driving one ampere into the emitter and reading the voltage that appears, with the signal source set to zero volts rather than removed.

Both halves of that matter. Driving a current and reading a voltage gives the impedance directly, with no divider to undo and no assumption about what the network looks like; it is the same probe the networks field uses for the diagonal entries of the same inverse. And zeroing the source rather than deleting it keeps the netlist identical — the source resistance is still in the circuit, which is the whole subject, and an “open-circuited input” would be a different measurement with an answer four hundred times larger.

The distinction is the same one the reciprocity essay had to make for the opposite reason, and it is worth carrying: what is being held fixed is part of the measurement, and two arrangements that differ only in that are two different quantities rather than two estimates of one.

What is checked

Three assertions, and the first two are the ones that would catch a wrong netlist.

That the textbook expression is an upper bound on the solved impedance at every source resistance the slider offers — a one-sided assertion, because a two-sided one would be a claim about how good the approximation is and this figure’s subject is where it stops being one.

That the voltage gain is below one and above a half, which is what makes the stage a follower and would fail immediately if the transconductance were stamped with the wrong sign or between the wrong nodes.

And that the load capacitance changes nothing at low frequency, to a part in a million, so that the peak above it is the stage’s own reactance meeting the load rather than the load being measured twice.

What the peak becomes two rungs up

An output impedance that rises to 67 ohms at 29 megahertz is a specification failing. The two essays above this one find the same quantity doing something a specification has no vocabulary for at all.

The input that pushes back looks in at the base instead of out at the emitter and finds a negative resistance — 1182 ohms of it at 3.4 megahertz for a nanofarad on the emitter, with nothing added to the model. A negative resistance is not an oscillator until a reactance cancels, and the base lead supplies it: with ten ohms of source the loop goes unstable above 74.9 nanohenries, which is seven centimetres of wire.

The resistance that is below zero then finds the same sign change at the terminal this essay measures: 5.5 Ω at direct current and −21.9 Ω at 257 MHz, with the sign belonging to the wiring rather than to the transistor — an ideal source at the base produces no negative band at all, and a hundred nanohenries of lead produces one from 110 to 301 MHz. So 4.7 to 100 pF on the emitter oscillates while 1 pF and 470 pF do not, which is a band of load capacitance with quiet ground on both sides of it.

Read backwards into this page, the peak measured here is the first sign of that. The rise is the current gain falling; the sign change is what happens when the same mechanism is driven a little further with a little more inductance in the way. Which is why the peak being worst in the middle of the slider matters: it cannot be avoided by making the source stiffer or softer, and the repair that does work is the counterintuitive one those essays measure — a worse source.

What a follower is being reached for instead of

Nineteen ohms rising to sixty-seven is worth comparing against the alternative, because the reason to use a follower at all is that the alternative is more expensive.

The node that is at ground for a while measures what a feedback loop achieves at the same job: a tenth of an ohm at direct current, which is two hundred times better than this stage, rising a decade per decade as the loop runs out and settling at 909 ohms — the feedback resistors in parallel, with the amplifier contributing nothing. So the loop is enormously better where it has gain and worse where it does not, and the two curves cross somewhere in the middle of the audio band for ordinary parts.

The follower’s advantage is that its low impedance is a current gain rather than a loop gain, so there is no crossover frequency, no phase margin and nothing to compensate. The load that gets inside the loop is what the loop pays for that: a metre of coaxial cable on its output takes a unity-gain inverter’s phase margin from ninety degrees to forty-five, and the repairs cost either regulation or a second feedback path. A follower driving the same cable has no margin to lose — which is why the two are used together, a loop for accuracy at low frequency and a follower inside it for current, and why this essay’s numbers are the ones that decide whether the combination works above a megahertz.

That combination has one property worth naming, because it is the reason the arrangement is ubiquitous. A follower inside a loop has its own output impedance divided by the loop gain, so the 19.08 ohms becomes a tenth of an ohm where the loop has gain — and the peak at 29 megahertz, which the loop has no gain to divide, survives unchanged. So the composite has the loop’s impedance at low frequency and the follower’s at high, and the crossover is wherever the loop gain passes unity: the frequency what is left at crossover is about, doing a job nobody usually credits it with.

Which is the useful thing to know about the peak. It is not a defect to be designed out, because nothing in the follower can move it; it is the composite’s high-frequency output impedance, it is where a capacitive load will resonate against it, and the design decision it feeds is what to put in series with the output rather than what to change about the transistor. Which is the same repair the resistor that buys the margin back measures for a loop, arrived at here for a stage with no loop in it at all — a resistance between an inductive source and a capacitive load, damping a resonance that neither of them has alone. The same component, for the same reason, in a circuit whose failure mode has a different name.

Part 1 on emitter follower

One argument about Emitter follower, and one of 4 essays on it so far, each part numbered by how much of the idea it assumes. What sits either side of it:

A follower with 1000 pF on it looks like -1182 Ω of negative resistance. computed by solving, not by drawing. The impedance looking into the base of an emitter follower carrying 5.0 mA, with 1000 pF on its emitter. The real part is negative from 1.25 MHz upward and reaches -1182 Ω at 3.40 MHz: the load's reactance multiplied by a complex current gain, with nothing added to the model. A negative resistance is not an oscillator until a reactance cancels, and the base lead supplies it — the total loop reactance passes through zero at a frequency the inductance chooses, and the loop resistance there goes negative above 74.9 nH with 10 Ω of source, which is a few centimetres of wire. A hundred ohms of source raises that to 913 nH: the repair is a resistor in the base, and it works by making the source worse. The input that pushes back Part 2 — An emitter follower with a capacitor on its emitter has a negative resistance looking into its base — 1182 ohms of it at 3.4 megahertz for a nanofarad, with nothing added to the model. A negative resistance is not an oscillator until a reactance cancels, and the base lead supplies it: with ten ohms of source the loop goes unstable above 74.9 nanohenries, which is seven centimetres of wire. The repair is the opposite of the instinct — a hundred ohms of source raises the threshold to 913 nanohenries, so the fix for a follower that oscillates is to make the thing driving it worse.

Where this goes next

Linearising an exponential at 27 °C, and what it costs. The linear model understates the gain by 1% at 7.30 mV and by 10% at 22.8 mV. The thermal voltage at this temperature is 25.9 mV, so "small compared with Vₜ" is not the criterion — 28% of Vₜ is already 1% wrong. How small is small signal Linearising an exponential replaces a curve by its tangent, which is exact at a point and progressively wrong away from it. The amplitude at which it is one per cent wrong is 7.3 millivolts at room temperature — 28 per cent of the thermal voltage, not a small fraction of it, and a good deal smaller than "small signal" suggests. 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. Two probes on a 2.0 kΩ source. computed by solving, not by drawing twice per frequency: the node alone, and the node with the probe's elements across it. The one-to-one probe's 115.0 pF makes the reading one per cent wrong at 6.79 kHz. The ten-to-one probe puts 12.8 pF in series with the cable, so its tip sees 11.5 pF and the same error arrives at 69.2 kHz — 10 times further up, bought with a factor of ten in signal — the two edges stand in the ratio of the tip capacitances, 10.00. At direct current neither probe is capacitive at all and the ten-to-one still reads 0.02% low, because 10 MΩ across 2.0 kΩ is a divider. The probe is part of the circuit A one-to-one oscilloscope probe on a two-kilohm source gives a reading that is one per cent wrong at 6.8 kHz. Not because the instrument is inaccurate — it is reading correctly — but because the hundred and fifteen picofarads at the end of the cable are across the node, and above that frequency the trace on the screen is a picture of a circuit that only exists while the probe is attached.

What links here

Essays that reach for this one mid-argument — the half of a link its own author cannot write down.

What this makes readable

Essays that name this one as a prerequisite.

The objects named here

The third axis, after the field and the idea: the things themselves, and every essay that touches each one.

Capacitive loadCurrent mirrorEmitter followerLoadingOutput impedanceParasiticsSmall-signal modelTransit frequency