220-A1.2

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  • 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.

Figure 1: A wideband voltage divider circuit.

Let and similarly . Thus, the output voltage can be expressed as:

 

 

 

 

(1)

Notice that we can cancel out the pole with the zero when we set , or equivalently,

 

 

 

 

(2)

Intuitively, we can think if this as a resistive voltage divider at low frequencies, and a capacitive divider with the same ratio at high frequencies. Thus, the output voltage will simply be equal to:

 

 

 

 

(3)

We can then build a simple 10X oscilloscope probe circuit with an input impedance of and an input capacitance of using , , , and . Since the pole and zero cancel each other out, the bandwidth of the probe circuit is not limited by its RC values.

A Lossy LC Tank

A Simple Switched-Capacitor Circuit