# Compensating Attenuator Probe

To improve matters, a variable capacitor is often added in parallel with the resistance of the attenuator, resulting in a compensated attenuator probe such as the one shown in Fig. 1. In Chapter 19, it was demonstrated that a square wave can be generated by a summation of sinusoidal signals of particular frequency and amplitude. If we therefore design a network such as the one shown in Fig. $1$ that will ensure that $V_{ \text {scope }}$ is $0.1 V_{i}$ for any frequency, then the rounding distortion will be removed, and $V_{ \text {scope }}$ will have the same appearance as $V_{i}$.
Fig. 1: Compensated attenuator and input impedance to a scope, including the cable capacitance.
Applying the voltage divider rule to the network of Fig. 1, $$\mathbf{V}_{\text {scope }}=\frac{\mathbf{Z}_{s} \mathbf{V}_{i}}{\mathbf{Z}_{s}+\mathbf{Z}_{p}} \tag{1}$$ If the parameters are chosen or adjusted such that $$R_{p} C_{p}=R_{s} C_{s}$$ the phase angle of $\mathbf{Z}_{s}$ and $\mathbf{Z}_{p}$ will be the same, and Equation (1) will reduce to $$\mathbf{V}_{\text {scope }}=\frac{R_{s} \mathbf{V}_{i}}{R_{s}+R_{p}}$$ which is insensitive to frequency since the capacitive elements have dropped out of the relationship. In the laboratory, simply adjust the probe capacitance using a standard or known square-wave signal until the desired sharp corners of the square wave are obtained. If you avoid the calibration step, you may make a rounded signal look square since you assumed a square wave at the point of measurement. Too much capacitance will result in an overshoot effect, whereas too little will continue to show the rounding effect.