# Effective use of filter capacitors to clean up voltage source signals in portable consumer designs

September 13, 2007

Portable consumer systems' sizes are becoming increasingly smaller. As a result, the available space between components is also becoming tighter, making it more difficult to effectively separate digital and analog circuits.

Generally, system design engineers have to use many capacitors to filter digital noise, expecting to get a clean voltage source as the power supply for analog circuits. This article discusses the effect of filter capacitors.

In most voltage regulators, there are always two capacitors, Cin and Cout (Figure 1 below).

 Figure 1: In most voltage regulators, there are always two capacitors, Cin and Cout.

The main purpose of Cin is to filter AC noise, suppressing voltage transition applied to the regulator's input. Meanwhile, Cout's role is to form loop compensation (adding a zero, improving phase margin and inevitably generating a pole) and suppress AC voltage transition due to dynamic load or input. In the sense of attenuating high frequency components, filtering AC noise and suppressing voltage transition are equivalent essentially.

Some characteristics of capacitors manufactured by different dielectrics vary. Understanding the six basic parameters to describe electronic circuits, components or materials is necessary before studying capacitor features.

Resistance (R). Expressed in ohm, it is the ratio of DC voltage to DC current throw conductor.

Reactance (X) . It is introduced by storage energy components, like capacitors or inductors in AC circuitry, including capacitance and inductance. It is expressed in ohm.

Impedance (Z) . Expressed in ohm, it is a complex quantity as it consists of a real part, resistance, and an imaginary part, reactance. It is also expressed as Z = R + jX.

Conductance (G) . It is the ratio of DC current to DC voltage, the reciprocal of resistance. It is expressed in siemens.

Susceptance (B) . It is an imaginary part of admittance, including BC and BL, and is expressed in siemens.

Admittance (Y) . It is the reciprocal of impedance and is expressed in siemens. Also a complex quality, its real part is conductance and its imaginary part is susceptance. It can also be expressed as Y = G + jB. Y is used to describe combinations of components in parallel.

 Figure 2: Impedance is usually used to describe components in series. Admittance is used to describe combinations of components in parallel..

Impedance is usually used to describe components in series (Figure 2, above). For a combination of components in series, if Phi is larger than 0 degrees, it means that it's inductive to device terminals - the closer to 90 degrees, the more inductive it is.

If Phi is 90 degrees, it is a pure inductor. If Phi is less than 0 degrees, it means that it's capacitive - the closer to -90 degrees, the more capacitive it is. If Phi is -90 degrees, it's a pure capacitor.

Table 1 above lists the features of the different types of capacitors according to dielectric classification.

 Figure 3: All devices have parasitic components - unwanted inductance in capacitors and resistors, unwanted resistance in capacitors etc.

There is neither pure resistance nor reactance in the real world, but a combination of these impedance elements. All devices have parasitic components such as unwanted inductance in capacitors and resistors, and unwanted resistance in capacitors. The equivalent circuit for real electrolytic capacitor is shown in Figure 3, above.

For multiple layer ceramic capacitors, its equivalent circuit is shown in Figure 4 below. For filter capacitors, it is good to keep them capacitive even at high frequency - never inductive. This means that Phi is equal or close to -90 degrees.

 Figure 4: For filter capacitors, it is good to keep them capacitive even at high frequency - never inductive. This means that Phi is equal or close to -90 degrees.

The capacitor's performance can be determined comprehensively if serial resistance (RS), serial capacitance (CS), serial inductance (LS), Z and Phi across two leads are obtained at different frequencies.

For a 50V/10 microfarad aluminum electrolytic capacitor, frequency exceeding 800kHz represents inductance instead of capacitance. Both ceramic capacitors have high Q and are still quite capacitive, even when frequency is close to 1MHz.

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