Capacitance Multipliers: How Circuits Make Small Capacitors Act Big

A capacitance multiplier is a circuit that makes a capacitor behave, from the outside, as if it were much larger than it really is. A 100 microfarad capacitor wired into the right transistor circuit can smooth a power supply about as well as a capacitor a hundred times its size. An op-amp circuit can turn a 1 microfarad film capacitor into the electrical equivalent of a 100 microfarad one for a slow timing circuit. Inside a chip, a few hundred picofarads of on-die capacitance can be made to act like several nanofarads in a phase-locked loop. And in a calibration laboratory, a precision transformer instrument can scale a 1 microfarad standard all the way up to an accurate 1 farad.

The Wikipedia summary of the subject divides capacitance multipliers into two families. Active multipliers use transistors or operational amplifiers and draw power from a supply. Passive multipliers use transformers (specifically, autotransformers or inductive voltage dividers) and are used mainly as laboratory reference standards. The active types are by far the more common, and they show up in three main places: power-supply ripple filters (notably for class-A audio amplifiers), low-frequency filters and long timing circuits, and integrated circuits where on-chip capacitors are expensive in silicon area.

This article explains what capacitance is doing in each case, how each kind of multiplier works, where the "multiplication" is real and where it is closer to a figure of speech, and what designers have to watch out for.

Why anyone needs a bigger capacitor

What a capacitor does

A capacitor stores electric charge. The charge Q it holds is proportional to the voltage V across it, and the constant of proportionality is its capacitance C:

Q = C × V

Capacitance is measured in farads (F). One farad is a very large amount for most electronic purposes, so practical values are usually given in microfarads (µF, millionths of a farad), nanofarads (nF, billionths) or picofarads (pF, trillionths).

Two properties of capacitors make large values useful.

• Impedance falls with frequency. A capacitor's opposition to alternating current, its reactance, is X_C = 1 / (2π f C). A larger capacitor has lower reactance at a given frequency, so it shunts more of an unwanted AC signal (such as power-supply ripple) to ground.
• Time constants grow with capacitance. A resistor R charging a capacitor C does so with a time constant τ = R × C. For long delays or very low-frequency filters, either R or C has to be large.

Why large capacitors are a problem

Physically large capacitors bring a series of practical troubles. They take up space and cost money. High-value electrolytic capacitors have relatively loose tolerances and leak some current. Precise, low-leakage types such as film capacitors become bulky and costly at high values. On an integrated circuit, the problem is sharper: a capacitor's area is roughly proportional to its capacitance, so a large loop-filter capacitor can dominate the size of a circuit block. An Analog Devices patent on PLL design (US 8,760,201) makes exactly this point, noting that because capacitor area is approximately proportional to capacitance, reducing the needed capacitance by a factor of N reduces the area to about 1/N.

A capacitance multiplier offers a way out: keep the physical capacitor small and let the circuit do the rest.

The general principle: scaling the current

Every capacitance multiplier relies on the same idea. A capacitor's defining behaviour is the relationship between the voltage across it and the current through it:

I = C × dV/dt

If a circuit arranges matters so that, for a given rate of change of voltage at its terminals, the current flowing in at those terminals is k times the current flowing through the internal capacitor, then the terminals behave like a capacitor of value k × C. Equivalently, the impedance seen at the terminals is the capacitor's impedance divided by k.

Different circuits achieve this scaling in different ways:

• A transistor multiplies the small current in its base by its current gain.
• An op-amp circuit uses a resistor ratio to set how much current flows in the terminal compared with the capacitor branch.
• An inverting amplifier with feedback capacitance (the Miller effect) makes the feedback capacitor look (1 + A) times larger at its input.
• A charge pump circuit in a PLL lets only a fraction of the charge reach the capacitor.
• A transformer scales voltage and current by its turns ratio, and impedance by the ratio squared.

The cost of the trick

None of these circuits creates free energy storage. In the active versions, the energy delivered to the load comes from the power supply through the active device; the small capacitor sets the behaviour but does not hold the energy that a real large capacitor would. This distinction is central to understanding what a capacitance multiplier can and cannot do, and it is discussed further in the section on misconceptions.

Transistor capacitance multipliers

The most widely built capacitance multiplier is a single bipolar transistor, or a Darlington pair, used to filter a DC power supply.

The circuit

The basic circuit has three parts.

1. A resistor feeds the transistor's base from the unregulated supply (the output of a rectifier and reservoir capacitor, which still carries ripple).
2. A capacitor from the base to ground forms an RC low-pass filter with that resistor, so the voltage at the base is a heavily smoothed copy of the input.
3. The transistor is wired as an emitter follower: the collector connects to the unregulated input, and the emitter delivers current to the load. The emitter voltage follows the base voltage, minus the base-emitter drop of roughly 0.65 volts.

The Electronics Notes description of the circuit puts it this way: the transistor "effectively multiplies the capacitance on the base by the current gain of the transistor." The Wikipedia article says the capacitor is multiplied by approximately the transistor's current gain β, and that the load on the capacitor is reduced by a factor of (β + 1). Viewed as an emitter follower, the input impedance looking into the base is

Z_in = R_load × (β + 1)

where R_load is the resistance seen at the emitter. The Wikipedia article writes this as Z_in = R₂ × (β + 1).

Why it works

The RC filter at the base only has to supply the transistor's base current, which is the load current divided by roughly (β + 1). Because that current is small, the resistor can be large and the capacitor small while still giving a long time constant and therefore heavy filtering. The transistor then amplifies that small, smooth base current into the full load current. From the load's point of view, the supply looks as if it had been filtered by a capacitor about β times larger.

Worked example (hypothetical values)

Suppose a transistor with current gain β = 100, a base capacitor C1 = 100 µF, a base resistor R = 470 Ω and a load current of 0.5 A. The input has ripple at 100 Hz (a full-wave rectified 50 Hz supply).

• Effective capacitance. About (β + 1) × C1 = 101 × 100 µF ≈ 10,100 µF, or roughly 10 mF.
• Base current. 0.5 A / 101 ≈ 4.95 mA.
• Filter corner frequency. f_c = 1 / (2π × 470 × 0.0001) = 1 / 0.2953 ≈ 3.39 Hz.
• Ripple attenuation at 100 Hz. For a first-order RC filter, |H| = 1 / √(1 + (f/f_c)²) = 1 / √(1 + (100/3.39)²) ≈ 1 / √(1 + 870) ≈ 1/29.5 ≈ 0.034. That is about −29 dB. One volt of ripple at the input becomes roughly 34 millivolts at the base, and the emitter follows the base.
• Voltage drop. The base current through the resistor drops about 4.95 mA × 470 Ω ≈ 2.3 V, plus about 0.65 V across the base-emitter junction. The output sits roughly 3 V below the input.
• Transistor dissipation. About 0.5 A × 3 V ≈ 1.5 W.

Now compare with a passive RC filter that has the same effect on the load. The equivalent is a resistor of R/(β + 1) ≈ 4.65 Ω in series with a capacitor of about 10 mF. That resistor, carrying the full 0.5 A, would also drop about 2.3 V. The transistor circuit therefore behaves like a large RC filter with the same time constant, built from a capacitor one hundredth the size. This is the clearest way to see what "multiplication" means here: both the resistance and the capacitance are transformed by the gain, but the time constant is preserved.

The example also shows the main design tension. With a simple transistor of β = 100, the base resistor drop is substantial. Using a Darlington pair, with a combined gain on the order of 1,000, cuts the base current tenfold and lets the designer either cut the drop or raise the resistance for better filtering.

Practical design points

Electronics Notes and Rod Elliott's Elliott Sound Products (ESP) Project 15 article, which has been revised several times since 1999, give a consistent set of practical rules.

• Add a resistor from base to ground. Electronics Notes recommends a bias divider in all cases. It lowers the base voltage, increases the voltage across the transistor and improves smoothing. Without it, the article reports odd ripple pulses as the capacitor approaches peak voltage. The divider current is suggested at about ten times the base current, so the emitter voltage stays stable across load currents.
• Leave headroom. The circuit only filters well when the transistor has enough voltage across it to stay out of saturation at the bottom of each ripple trough. Electronics Notes gives the output as roughly 2 to 3 V below the input under load, with a minimum drop of about 3 V across the series transistor. ESP's Project 15 says up to 3 V may be lost across the multiplier, with a minimum input-to-output differential of 1 to 2 V, and recommends 6 to 10 V for class-AB amplifier use.
• Account for dissipation. The pass transistor dissipates the load current times the voltage across it. ESP's design dissipates under 4 W per output transistor at 1.25 A continuous.
• Protect the transistor. A diode prevents reverse bias of the transistor when the input collapses faster than the output, and an output capacitor improves decoupling and stability.
• Expect slow turn-on. Large values of the base resistor and capacitor reduce ripple but slow the output's rise when power is first applied, because of the long time constant.

The ESP design in numbers

ESP Project 15 is a well-known hobbyist and professional reference design for a class-A amplifier supply. Its stated targets and results include:

The article also recommends a toroidal transformer rated at least five times the amplifier power and a heatsink of about 5 °C/W or better per output device, and it stresses star-earth wiring because poor grounding or ripple re-injection causes hum.

"There is no multiplication"

One point in ESP's article is worth dwelling on because it corrects a common way of describing these circuits. Elliott writes that "there is no multiplication of the capacitance in the circuit." His point is that the circuit is a buffered filter: an RC filter at the base, followed by a high-gain current amplifier. The "multiplied capacitance" is a convenient way of describing the result from the load's point of view, not a physical change in the capacitor. Both views are correct; they simply describe the same circuit at different levels. The Wikipedia article's framing (the capacitor appears multiplied by about β) and Elliott's framing (it is a filter plus a buffer) lead to the same design equations.

Comparison with a voltage regulator

A capacitance multiplier looks superficially like a linear voltage regulator, and in many designs the two are alternatives. They behave differently, however.

ESP's Project 15 gives a concrete comparison. For a 20 V output at 1.25 A average, a regulator needs about 23 V minimum input, so the transformer must provide about 22 V RMS. With a regulator input ranging from 25.4 V to 35 V depending on mains voltage, regulator dissipation would be 6.75 W at minimum input and 18.75 W at maximum, with about 37 W at the 2.5 A peak. The capacitance multiplier dissipates far less, but it does not regulate, so the output voltage and amplifier power vary with mains voltage. Elliott also notes that class-AB amplifiers, with their highly variable current demands, are poorly suited to the circuit unless a large output capacitor and a larger voltage differential are used.

Electronics Notes makes the same point more briefly: the circuit is "not a voltage regulator," and its output follows the input with no reference.

MOSFET versions

ESP added a MOSFET version of the circuit in 2016. Compared with the bipolar version, Elliott reports roughly 10 dB better hum attenuation with a constant load, but transient hum breakthrough at least 20 dB worse, slower recovery (around 500 ms compared with under 200 ms), higher dissipation for the same current, the need for a zener diode between gate and source for protection, and limited safe operating area in linear mode that must be checked against the datasheet.

Where transistor multipliers are used

Electronics Notes lists typical uses where low noise matters: after linear or switch-mode regulators, in PLL-based RF circuits, around data converters, and in hi-fi preamplifiers. The Wikipedia article highlights power supplies for class-A amplifiers, where the constant, high quiescent current makes a large passive filter capacitor bulky and where hum in the supply would be heard directly in the output.

Operational amplifier capacitance multipliers

Where the goal is not to filter a power supply but to create a large, precise, low-leakage capacitance for a filter or timer, op-amp circuits are used. They are described in the Wikipedia article and appear in the Texas Instruments "AN-31 amplifier circuit collection" (document SNLA140D, revised October 2020), which began life as National Semiconductor Application Note AN-31. The current TI edition includes a "Capacitance Multiplier" circuit and a "Two-Stage Capacitance Multiplier," along with a "Simulated Inductor," each with downloadable TINA-TI simulation files.

The basic single op-amp circuit

In the simplest version described by Wikipedia, the multiplied capacitance seen at the input node is

C = C₁ × (R₁ / R₂)

Choosing R₁ much larger than R₂ yields a large effective capacitance. The trade-offs, according to the Wikipedia article, are a series resistance of roughly R₂ in the equivalent circuit, and a leakage current across the synthesised capacitance caused by the op-amp's input offsets. The series resistance means the result is not an ideal capacitor but a capacitor in series with a resistor, which limits how well it works at higher frequencies.

Worked example (hypothetical values). Take C₁ = 0.1 µF, R₁ = 100 kΩ and R₂ = 100 Ω. Then C ≈ 0.1 µF × (100,000 / 100) = 100 µF, with roughly 100 Ω of series resistance. For a slow filter or timer, 100 Ω may be negligible next to the other resistances in the circuit. For a power-supply bypass, it would be useless.

The improved two op-amp circuit

A second circuit described in the Wikipedia article uses two op-amps and gives

C = C₁ × (1 + R₂ / R₁)

The Wikipedia article says this version avoids both the series resistance and the offset-induced leakage of the simpler circuit, and that it allows the capacitance to be varied by changing a resistor. A JoVE design example describing a two-amplifier version uses one op-amp as a voltage follower and the second as an inverting amplifier.

Worked example (hypothetical values). With C₁ = 1 µF, R₁ = 1 kΩ and R₂ = 99 kΩ, the effective capacitance is 1 µF × (1 + 99) = 100 µF. Replacing R₂ with a potentiometer turns this into a variable capacitor covering a wide range, something no physical capacitor of this size can do.

Timing application. Used with a 1 MΩ timing resistor, a 100 µF synthesised capacitance gives a time constant of 1,000,000 × 0.0001 = 100 seconds, from a 1 µF film capacitor that is far smaller, cheaper and lower-leakage than a 100 µF component.

Floating and negative capacitance

The Wikipedia article notes two further variations.

• Floating multipliers. The basic circuits have one terminal grounded. Floating versions, in which neither terminal is tied to ground, are possible with additional circuitry.
• Negative capacitance. A negative impedance converter (an op-amp circuit that inverts the sign of an impedance) can make a capacitor look negative. A negative capacitance can partly cancel unwanted positive capacitance, for example the capacitance of a cable or a sensor input.

Limits of op-amp multipliers

The op-amp versions inherit the limits of the op-amps themselves.

• Voltage range. The synthesised capacitor can only operate within the op-amp's output voltage swing, set by its supply rails.
• Current range. The current the synthesised capacitor can deliver is limited by the op-amp's output current capability. A synthesised 100 µF capacitor cannot deliver the surge current that a real 100 µF electrolytic could.
• Frequency range. The op-amp's gain falls with frequency, so the multiplication works only well below the amplifier's bandwidth.
• Offsets and noise. Input offset voltages and currents cause leakage-like errors, and the op-amp's own noise appears across the synthesised capacitance.

These limits mean op-amp capacitance multipliers belong in signal-level circuits: filters, timers, oscillators and integrators.

The Miller effect: capacitance multiplication by accident and by design

Long before designers set out to multiply capacitance on purpose, they ran into it by accident. In 1920, John Milton Miller, publishing in the Scientific Papers of the US Bureau of Standards, described how the small capacitance between the input and output of a vacuum-tube amplifier is magnified by the amplifier's gain. The Wikipedia article on the Miller effect notes that the history section dates the work to 1919, while the cited paper is dated 1920.

For an inverting amplifier with gain −A_v and a capacitance C connected between its input and output, the capacitance seen at the input is

C_M = C × (1 + A_v)

and, more generally, an impedance Z bridging input and output looks like Z / (1 + A_v) at the input.

Worked example (hypothetical values). A 10 pF capacitance across an inverting stage with a gain of 99 appears at the input as 10 pF × (1 + 99) = 1,000 pF, or 1 nF.

In amplifier design, the Miller effect is often a nuisance, because it slows high-frequency response. But it can be used deliberately. The Wikipedia article states that "the Miller effect may also be exploited to synthesize larger capacitors from smaller ones," and gives the example of stabilising feedback amplifiers, where the required compensation capacitance may be too large to include practically, especially on integrated circuits where capacitors consume significant area. The internal compensation capacitor in many op-amps works this way.

The gyrator: the inverse trick

A close relative of the capacitance multiplier is the gyrator, a circuit that makes a capacitor behave like an inductor. Bernard Tellegen proposed the gyrator in 1948 as a hypothetical fifth linear circuit element, alongside the resistor, capacitor, inductor and ideal transformer, according to the Wikipedia article on gyrators.

In the common op-amp version, a resistor and capacitor form a differentiating network whose voltage, buffered by an op-amp follower and fed back through a resistor R_L, makes the input look like an inductor of value L = R_L × R × C in series with a resistance R_L. The TI AN-31 collection includes this "Simulated Inductor" right next to its capacitance multipliers.

Gyrators share the limits of active capacitance multipliers. The Wikipedia article on gyrators lists several: they work only at low frequencies and low power; their impedance levels off rather than rising indefinitely with frequency; they cannot produce the high-voltage flyback spike of a real inductor because the voltage is limited by the supply; they do not create or respond to magnetic fields; and their parasitic series resistance is much higher than a physical inductor's. The parallel with capacitance multipliers is exact: an active circuit can mimic the small-signal behaviour of a component, but not its energy storage or its behaviour beyond the circuit's supply limits.

Capacitance multiplication on integrated circuits

On a silicon chip, a capacitor is typically built from layers of metal or polysilicon separated by thin insulator, and its value per unit area is limited by the process. Phase-locked loops (PLLs), which generate clock and radio frequencies in almost every modern chip, need a loop-filter capacitor large enough to give the loop the right bandwidth and stability. That capacitor can be one of the largest components in the PLL.

The charge pump approach

A PLL's charge pump delivers pulses of current to the loop-filter capacitor in proportion to the phase error between the reference and the divided-down oscillator output. One way to make a small capacitor behave like a large one is to deliver only a fraction of each charge pulse to it.

US Patent 8,760,201, "Digitally programmed capacitance multiplication with one charge pump," filed 11 March 2013 by Ting Gao and Jiefeng Yan and assigned to Analog Devices, describes such a scheme. A blocking circuit lets only 1/N of the phase-error pulses charge or discharge the integral capacitor, so a capacitor C behaves as if it were N × C. The patent gives examples with N = 2, 4 and 8, and the factor can be programmed digitally.

Worked example from the patent. A traditional PLL in the patent's simulation used a 6.4 nF integral capacitor. The single-pump design used a 400 pF capacitor with a 1/16 blocking factor: 400 pF × 16 = 6.4 nF. Because capacitor area is roughly proportional to capacitance, the patent states that this reduces the capacitor area to about 1/16. The simulation used a 5 µA charge-pump current, a 40 MHz/V oscillator gain, a division ratio of 2,048, an 8 kHz reference, a damping factor of 0.9375 and a 75 kΩ resistor.

The same goal, reducing loop-filter area, has driven a line of academic work. A 2024 paper in IEEE Transactions on Circuits and Systems I by Kar and colleagues describes a 14 GHz sub-sampling PLL that replaces the conventional loop-filter capacitor with a multiplier circuit to reduce area.

Passive capacitance multipliers: transformer standards

The second family in the Wikipedia classification uses no amplifiers at all. Instead, precision transformers scale the voltage applied to a small, very accurate capacitor, and therefore the current it draws.

How transformer scaling works

An ideal transformer with turns ratio n scales voltage by n and current by 1/n, and so scales impedance by n². If a capacitor sits on one side of a transformer, the impedance seen from the other side is scaled accordingly, which is the same as scaling its capacitance. Using two transformers in combination, as the Wikipedia article describes, lets a small, high-precision capacitor be presented as an accurate large value.

The General Radio / IET Labs 1417

The Wikipedia article cites the General Radio (now IET Labs) 1417 as an example. IET Labs describes it as using "two precise inductive voltage dividers used to scale the value of the 1 µF capacitor up to 1 F in decade steps." The published specifications include:

The ratio and dissipation-factor accuracy vary by range:

Worked example. Scaling 1 µF to 1 F is a factor of 1,000,000, or six decades. The instrument covers this in six switch steps, each a factor of ten.

The table illustrates a general truth about multiplication: the error grows as the multiplication factor grows. The 10 µF setting is good to 0.02 percent at power frequencies, while the 1 F setting is good to 0.25 percent and is not specified at 1 kHz at all.

Limits of transformer multipliers

The Wikipedia article makes three points about this family. These instruments are reference standards for calibrating capacitance meters and bridges, not general-purpose circuit elements. They are four-terminal devices, which means they must be connected with separate current and voltage leads to get their rated accuracy. And they cannot be used at DC, because transformers do not pass direct current. IET Labs adds that the instrument can serve as a two-terminal standard at low frequency, with the dissipation factor below 1 for values up to 1,000 µF at frequencies below 150 Hz.

Choosing a type: a comparison

Design considerations in more depth

Noise

A capacitance multiplier filters only what passes through its RC network. Noise generated by the active device itself, and noise on the device's control terminal, appears at the output. In a transistor multiplier, the transistor's own noise and any ripple reaching the base through stray coupling set the floor. ESP's emphasis on star earthing and short, heavy connections from the transformer centre tap to the capacitor common point reflects the fact that wiring layout often matters more than the theoretical attenuation.

Load transients

In a transistor multiplier, a sudden jump in load current changes the base current demand and the voltage drop across the transistor. If the transistor is pushed into saturation during a ripple trough, the filtering effectively vanishes for that moment and ripple appears at the output. This is why ESP recommends larger differentials and a large output capacitor for amplifiers with highly variable current demands.

Start-up behaviour

Because the multiplier's output tracks a heavily filtered base voltage, it rises slowly at power-up. Electronics Notes notes that larger values of R and C reduce ripple but slow the output's rise. In some designs, a slow start is welcome, because it softens inrush and turn-on thumps in audio equipment. In others, it may interfere with power sequencing.

Stability and frequency response

Op-amp multipliers are feedback circuits and can oscillate if poorly laid out or loaded with the wrong impedance. Their multiplication factor holds only over the frequency range where the op-amp has plenty of loop gain. Above that, the synthesised capacitance gradually stops looking like a capacitor.

Thermal design

For power multipliers, the pass device's dissipation equals the load current times the voltage across it, and must be removed by a heatsink. ESP's design aims for under 4 W per device at 1.25 A, with a heatsink of about 5 °C/W or better.

Common misconceptions

"A capacitance multiplier stores more energy." The energy stored in a capacitor is ½ C V². In an active multiplier, the small physical capacitor still stores only the energy its real capacitance allows. The large current delivered to the load comes from the power supply through the transistor or op-amp. If the supply fails, the multiplier cannot ride through the interruption the way a genuinely large reservoir capacitor could.

"It regulates the voltage." A transistor capacitance multiplier smooths ripple but has no reference voltage. Its output follows the average input voltage, so it rises and falls with mains voltage and with load. Electronics Notes and ESP both stress this.

"It is a free lunch for ripple." The filtering comes at the cost of a voltage drop of a few volts and the corresponding power dissipation in the pass device. In the worked example above, the multiplier dropped about 3 V and dissipated 1.5 W to achieve its filtering.

"The capacitor is physically multiplied." As ESP's Rod Elliott puts it, "there is no multiplication of the capacitance in the circuit." The multiplication describes how the circuit appears to the load or to the surrounding circuit. Internally, a small capacitor filters a small current.

"Bigger multiplication is always better." Higher multiplication factors magnify errors, leakage and noise along with capacitance. The IET 1417's accuracy table shows this even for a precision transformer instrument, and op-amp versions show it through offset-induced leakage.

"It works at any frequency." Active multipliers work only below the bandwidth of their amplifiers, and transformer multipliers work only on AC. Each type has a band where it behaves like a capacitor and regions where it does not.

A short history

The ideas behind capacitance multiplication developed alongside amplifying electronics.

Frequently asked questions

What is a capacitance multiplier in one sentence? A circuit that makes a capacitor appear larger to the rest of a circuit, by scaling the current that flows at its terminals relative to the current through the actual capacitor.

How much can a transistor multiply capacitance? By roughly its current gain, β. A transistor with β = 100 makes a capacitor look about 100 times larger; a Darlington pair with a combined gain around 1,000 makes it look about 1,000 times larger.

Is a capacitance multiplier the same as a voltage regulator? No. It removes ripple but does not hold the voltage at a fixed value. Its output follows the average input voltage.

Why are capacitance multipliers popular in audio amplifiers? Class-A amplifiers draw a large, steady current, so ripple on the supply directly causes audible hum. A multiplier gives heavy ripple rejection without an enormous filter capacitor or the higher dissipation of a regulator. ESP's design reports output ripple around 1 mV RMS with a real class-A amplifier, more than 50 dB below the raw supply.

What formula gives the op-amp multiplier's capacitance? For the basic single op-amp circuit described on Wikipedia, C = C₁ × (R₁/R₂). For the improved two op-amp circuit, C = C₁ × (1 + R₂/R₁).

Can I make a negative capacitor? Yes, in the sense of a circuit whose terminal behaviour is that of negative capacitance, using a negative impedance converter. It is useful for cancelling unwanted capacitance.

Why use a 1 F transformer standard instead of a 1 F capacitor? Large real capacitors are not accurate or stable enough to serve as calibration references. A transformer standard derives its large values from a precise 1 µF capacitor and accurate transformer ratios, giving known values traceable to the small standard.

Do capacitance multipliers work at DC? Active ones work on DC supplies (the transistor type is built for exactly that), but the synthesised capacitance only exists for changing voltages, which is all any capacitor responds to. Transformer standards cannot be used at DC at all.

Why do chip designers care? Because on-chip capacitors take up silicon area roughly in proportion to their value. Multiplying a small capacitor by 16, as in the Analog Devices patent example, can cut the capacitor area to about one sixteenth.

What is the relationship to the Miller effect? The Miller effect is a form of capacitance multiplication that happens naturally when a capacitance bridges the input and output of an inverting amplifier. It makes the capacitance look (1 + A) times larger, and designers can exploit it on purpose.

Summary

Capacitance multipliers answer a simple problem: large capacitors are bulky, expensive, imprecise or, on a chip, simply too large. By scaling the current at a circuit's terminals relative to the current in a small capacitor, a transistor, op-amp, amplifier gain, charge pump or transformer can make that small capacitor behave like a large one. The transistor version is a workhorse of low-ripple power supplies, especially for class-A audio; op-amp versions create large, precise capacitances for filters and timers; Miller and charge-pump techniques save silicon area; and transformer standards provide accurate capacitance up to 1 farad for calibration. In every active case, the multiplication describes behaviour, not stored energy, and comes with costs in voltage drop, dissipation, noise, bandwidth and accuracy that the designer must weigh.

Sources

• Capacitance multiplier (Wikipedia)
• Texas Instruments, AN-31 amplifier circuit collection (SNLA140D)
• Rod Elliott, Elliott Sound Products, Project 15: Capacitance Multiplier Power Supply
• Electronics Notes, Transistor Capacitance Multiplier Circuit
• IET Labs, GenRad 1417 Capacitance Standard 1 µF to 1 F
• IET Labs, 1417 instruction manual
• US Patent 8,760,201, Digitally programmed capacitance multiplication with one charge pump (Google Patents)
• Miller effect (Wikipedia)
• Gyrator (Wikipedia)
• JoVE, Design example: capacitance multiplier circuit