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A capacitance multiplier is designed to make a
Here the capacitance of capacitor C1 is multiplied by approximately the transistor's current gain (β).
Without Q, R2 would be the load on the capacitor. With Q in place, the loading imposed upon C1 is simply the load current reduced by a factor of (β + 1). Consequently, C1 appears multiplied by a factor of (β + 1) when viewed by the load.
Another way is to look at this circuit as an emitter follower with capacitor C1 holding voltage at base constant with load of input impedance of Q1: R2 multiplied by (1 + β), so the output current is stabilized much more against power line voltage noise.
Here, the capacitance of capacitor C1 is multiplied by the ratio of resistances: C = C1 * R1 / R2 at the Vi node.Op Amp Circuit Collection, National Semiconductor Application Note AN-31, reproduced in National Semiconductor Applications Handbook, 1994, p. 86.
The synthesized capacitance also brings a series resistance approximately equal to R2, and a leakage current appears across the capacitance because of the input offsets of OP. These problems can be avoided by a circuit with two op amps. In this circuit the input to OP1 can be a.c.-coupled if necessary, and the capacitance can be made variable by making the ratio of R1 to R2 variable. C = C1 * (1 + (R2 / R1)).
In the circuits described above the capacitance is grounded, but floating capacitance multipliers are possible.
A negative capacitance multiplier can be created with a
IET Labs 1417 FOUR-TERMINAL CAPACITANCE STANDARD
Electricity Electronic circuits
capacitor
A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals.
The effect of a ...
function like a much larger capacitor. This can be achieved in at least two ways.
* An active circuit, using a device such as a transistor or operational amplifier
* A passive circuit, using autotransformer
An autotransformer is an electrical transformer with only one winding. The " auto" (Greek for "self") prefix refers to the single coil acting alone, not to any kind of automatic mechanism. In an autotransformer, portions of the same winding act ...
s. These are typically used for calibration standards. The General Radio / IET labs 1417 is one such example.
Capacitor multipliers make low-frequency filters and long-duration timing circuits possible that would be impractical with actual capacitors. Another application is in DC power supplies
A power supply is an electrical device that supplies electric power to an electrical load. The main purpose of a power supply is to convert electric current from a source to the correct voltage, current, and frequency to power the load. As a r ...
where very low ripple voltage (under load) is of paramount importance, such as in class-A amplifiers.
Transistor-based
Here the capacitance of capacitor C1 is multiplied by approximately the transistor's current gain (β).
Without Q, R2 would be the load on the capacitor. With Q in place, the loading imposed upon C1 is simply the load current reduced by a factor of (β + 1). Consequently, C1 appears multiplied by a factor of (β + 1) when viewed by the load.
Another way is to look at this circuit as an emitter follower with capacitor C1 holding voltage at base constant with load of input impedance of Q1: R2 multiplied by (1 + β), so the output current is stabilized much more against power line voltage noise.
Operational amplifier based
Here, the capacitance of capacitor C1 is multiplied by the ratio of resistances: C = C1 * R1 / R2 at the Vi node.Op Amp Circuit Collection, National Semiconductor Application Note AN-31, reproduced in National Semiconductor Applications Handbook, 1994, p. 86.
The synthesized capacitance also brings a series resistance approximately equal to R2, and a leakage current appears across the capacitance because of the input offsets of OP. These problems can be avoided by a circuit with two op amps. In this circuit the input to OP1 can be a.c.-coupled if necessary, and the capacitance can be made variable by making the ratio of R1 to R2 variable. C = C1 * (1 + (R2 / R1)).
In the circuits described above the capacitance is grounded, but floating capacitance multipliers are possible.
A negative capacitance multiplier can be created with a negative impedance converter
The negative impedance converter (NIC) is an active circuit which injects energy into circuits in contrast to an ordinary load that consumes energy from them. This is achieved by adding or subtracting excessive varying voltage in series to the volt ...
.
Autotransformer based
These permit the synthesis of accurate values of large capacitance (e.g., 1 F) by multiplying the capacitance of a high-precision lower value capacitor by the use of two transformers. Its function acts as a reference standard, not as a general-purpose circuit element. The resulting device is a four-terminal element and cannot be used at dc.References
{{ReflistIET Labs 1417 FOUR-TERMINAL CAPACITANCE STANDARD
Electricity Electronic circuits