# Designing a Capacitance Multiplier as a Power Supply Filter

*All these components are important parts of your power conditioning strategy*

I always like to get down to the gritty details of different circuits, and I enjoy building them myself on a breadboard. Filtration and amplifier circuits are always fun to play with. There are some interesting linear circuits that can be used to decrease the noise floor in a circuit by removing noise from a power supply’s output.

An excellent circuit that can remove residual ripple voltage and other noise sources is a capacitance multiplier. A capacitance multiplier is a deceptively simple circuit for power conditioning and removing ripple on the output from a power supply. In terms of design and layout, you can easily design a capacitance multiplier from discrete components or an operational amplifier IC. This circuit causes a capacitor to behave like a much larger capacitor, which provide much better smoothing in power supply circuits.

## Capacitor Multiplier with a Transistor

The first way to build a capacitance multiplier circuit is to use an FET (or MOSFET). A transistor with higher DC gain (beta value) provides a larger capacitance multiplication factor in a capacitance multiplier circuit, thus BJTs are not normally used in capacitance multipliers as their gain is ~1. Note that a capacitance multiplier, whether or not it uses a transistor, is not a voltage regulator, although it can certainly be used in conjunction with a standard linear regulator (on the input or output) or a switching regulator (normally on the input). This circuit is inherently nonlinear and takes advantage of saturation in a transistor.

A simple capacitance multiplier circuit with a transistor is shown in the figure below. In this circuit, the two resistors function as a voltage divider that regulates the voltage applied to the base of the transistor and the voltage drop across the transistor. Simple capacitance multiplier circuits sometimes omit R2 to provide higher output voltage, but this reduces the level of noise suppression provided by this circuit. By using R2 in parallel with the capacitor, the transistor is more easily driven into saturation as the collector-base voltage is lower, thus the output from the transistor will saturate at a lower level. However, this increases the collector-emitter voltage drop, which increases power dissipation as heat.

*Simple capacitor multiplier with a transistor*

Driving the transistor to saturation is important here as this suppresses ripple on the input voltage from changing the output voltage. If you are driving the capacitance multiplier at a lower input voltage, then you need to apply a lower collector-base voltage (i.e., R2 > R1) to ensure the transistor enters saturation. If the input voltage is sufficiently high, you can set the output voltage by adjusting the values of R1 and R2.

With this circuit, the capacitance C is amplified to (1 + beta)*C, where beta is the gain provided by the transistor. In other words, the capacitor C behaves as if its capacitance is (1 + beta)*C. While the gain of a single transistor is limited, you can provide much higher capacitance multiplication factors by using a Darlington pair.

## Capacitor Multiplier with on Operational Amplifier

A capacitor multiplier can also be built with an operational amplifier instead of a transistor. In this case, the operational amplifier must be operating in the linear regime, i.e., the inputs must be unsaturated. This limits the range of input voltage values you can use in your capacitance multiplier circuit. Capacitance amplification factors of ~100 or larger are possible with this circuit, where the amplification factor is equal to the gain in the amplifier circuit, as long as the amplifier does not enter saturation. If the gain is less than 1, then this circuit could be viewed as a capacitance divider. This circuit is shown below.

*Capacitance multiplier with an operational amplifier.*

This circuit is intended to amplify the capacitance in a series RC circuit (R2 and C in series), effectively creating a much more powerful low pass filter. If you are looking to design a capacitance multiplier with an operational amplifier, you can generate a number of Bode plots with different values of C in order to examine the filtration provided by this circuit.

## Why Use a Capacitance Multiplier in a PCB?

Working with a capacitance multiplier provides the same level of filtration and smoothing as a much larger capacitor using smaller discrete components. Extremely strong low pass filtering with an RC circuit requires one or more large capacitors to provide strong rolloff, which consumes a large amount of board space. Alternatively, you could build a higher order low pass filter from stages using discrete components, but you still have the same problem, and you will need to set the 3 dB frequency to a very low value to properly filter ripple. This provides better ripple suppression, but it still uses a significant amount of board space.

Using a properly designed capacitance multiplier saves space on your board for other important components and circuits. Although the tradeoff in these circuits is heat generated in the transistor or amplifier and the limitations on the voltage levels that can be input to the circuits, this is normally not so severe that you need to include bulky thermal management measures in your board unless you are working at very high voltage. You can get an idea of the reliability of your capacitance multiplier using smoke analysis.

When you need to build a capacitance multiplier or any other circuit for power conditioning, you need PCB design and analysis software that includes a full suite of layout and simulation tools. Allegro PCB Designer and Cadence’s full suite of analysis tools make it easy to perform important power and signal integrity simulations with your circuits, offering a comprehensive view of their behavior.

If you’re looking to learn more about how Cadence has the solution for you, talk to us and our team of experts.