# How to Design an RC Circuit to Smooth a PWM Signal

By J.T. Barett
oscilloscope waveform image. image by Ken Pilon from <a href='http://www.fotolia.com'>Fotolia.com</a>

Pulse-Width Modulation techniques can improve the efficiency of amplifier and other signal-processing circuit designs. An analog signal, such as from sound, modulates the width of a pulse having a frequency over 100,000Hz. The circuit then amplifies or transmits the pulse. The last step gets rid of the pulse using a simple resistor-capacitor low-pass filter. It removes any high-frequency signals, such as the pulse wave, leaving only the original analog content. To design the RC circuit, you need to know the pulse's frequency.

#### Step 1

Select a capacitor value with which you'd like to work. For example, you can arbitrarily choose 1 nanofarad.

#### Step 2

Calculate the value of the resistor in the lowpass filter. Use the following formula:

R = 1 / (2 x pi x C x Fp) where R is the resistor's value in ohms, pi is 3.1416, C is capacitance in farads and Fp is the pulse's frequency in hertz. If the capacitance is 1 nanofarad and the frequency is 100,000Hz, then resistance works out to 1,600 ohms.

#### Step 3

Compare the calculated resistance value to the available EIA E24 standard resistor values. Since 1,600 ohms, or 1.6K ohms, is already a standard value, you can use that. Otherwise, use the next closest value resistor.

#### Step 4

Sketch the RC lowpass filter circuit. Draw the horizontal zigzag symbol for the resistor. Connected to the resistor, draw a short horizontal line. Two inches underneath, draw a parallel line as long as the resistor and top line. Connect a vertical capacitor symbol between the two parallel lines.

#### Step 5

Label the resistor on the sketch with the resistance value you calculated, and the capacitor with the capacitance value you chose.