Introduction to RC Networks

All electronic circuits include a resistor-capacitor (RC) network of some form. Even if all resistors and capacitors were intentionally left out of a circuit, there would still be stray resistances and capacitance associated with it. The RC combination is probably the most basic configuration used in circuit designs.

Resistor-capacitor combinations can be connected as either series or parallel, but the series combination is by far the most common form, as it can provide a variety of useful functions. Depending on whether the output voltage is taken off the resistor or capacitor, they can be used as either a high-pass or low-pass filter respectively. When used as a high-pass filter, the network tends to pass alternating current (AC), while blocking direct current (DC). The opposite action takes place in a low-pass filter, where alternating current is blocked and direct current is passed.

RC circuits are often found as coupling networks, compensating networks, power supply filters, and many others. Some circuit analysis for RC networks is an essential part of any circuit design. Since the resistor and capacitor are both passive components, the response on the output to a particular input can be calculated with good accuracy.

There are definite mathematical relationships between voltage and current for both resistors and capacitors. This relationship is linear for a resistor by using the familiar Ohm’ law:  V = IR.  But in a capacitor, there is no linear relationship between voltage and current, but there is a linear relationship between the charge on a capacitor and the voltage across it according to the equation Q = CV, where Q is the electrical charge on a plate of a capacitor, and C is the capacitance. The capacitance is a measure of the amount of charge that can be stored on each plate for a given potential difference or voltage which appears across its two terminals. This can be compared to resistance, R, which is measure of how much current can flow through it for a given voltage.

For a capacitor, the current is found to be proportional to the rate of change of the applied voltage rather than the voltage itself, like in a resistor. This can be put into the form:

I = C dv/dt.

This can be proven by assuming that I = dQ/dt, so dQ/dt = C dv/dt, and this simplifies to C dv = dQ. Then by integrating both sides, the result would be the basic form:  Q = CV. It can be seen that time is an important factor for capacitors, while time has no effect on the voltage-current relationship for resistors.

There is no power dissipated in a capacitor like there is in a resistor. The energy dissipated per unit time in a resistor (power) is: P = VI = I2 R = V2/R. This energy is released in the form of heat. But in a capacitor, the power supplied to it is stored as an electric field in the dielectric material between the two plates. For an ideal capacitor, there is no energy dissipated, but can only be stored until this energy can be sent to associated resistances in the circuit where it is dissipated as heat. The energy stored in a capacitor can be found to be ½CV2, and depends only on the capacitance and the potential difference appearing between the plates. It does not depend on the current, as was the case for resistors. These calculations assume an ideal capacitor with no internal leakage resistances, temperature coefficients, etc. But all capacitors normally have some leakage resistance through the dielectric material, so there is a small power loss because of this.

A designer might consider using an RL (resistor-inductor) network which would be equivalent to an RC network. But in the final design, the designer would almost always prefer using an RC network over an equivalent RL network for coupling networks, etc. because capacitors offer several advantages over inductors. Capacitors are easier to manufacture, they are lower in cost, take up much less space, and have negligible stray effects, such as internal resistance. Another consideration is the fact that a capacitor stores its energy in an electric field while the inductor stores its energy in a magnetic field. If there are two or more inductors used in a circuit, they could easily interfere with one another through this magnetic field generated. On the other hand, capacitors tend to contain their electric fields within their respective packages, which would allow components to be packed closely together without any concern about interference.

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