220-A1.2

• Activity: Simulating simple RLC circuits
• At the end of this activity, the student should be able to:

1. Run DC, AC, and transient simulations using ngspice.

A Wideband RC Voltage Divider

One way to build high-speed circuits with relatively large input impedances and capacitances is to use a simple RC voltage divider, as shown in the figure below. This RC divider is commonly found in oscilloscope 10X probes.

Let $Z_{1}=R_{1}\|{\frac {1}{j\omega C_{1}}}$ and $Z_{2}=R_{2}\|{\frac {1}{j\omega C_{2}}}$, then the output voltage can be expressed as:

$v_{out}={\frac {Z_{1}Z_{2}}{Z_{1}+Z_{2}}}\cdot v_{in}$

(1)