Measuring Probe Capacitance

 

An important but often overlooked oscilloscope characteristic is probe input impedance. An ideal oscilloscope would have an infinitely large input impedance so that the circuit being measured would be completely unaffected by the presence of the probe. Unfortunately, real oscilloscopes don't have an infinitely high input impedance. It is important to understand how the probe can affect signals being measured so you can be certain that the probe isn't causing measurement errors.

Probe input impedance is modeled as the parallel combination of a resistance and capacitance. Most oscilloscopes have a probe input resistance of either 1M or 10M ohms, and an input capacitance from less than a pico Farad (active FET probes) all the way up to 100 pF (low bandwidth passive probes). The resistive component is generally of little concern if the source impedance of the signal being measured is less than 10K (this would be a 1% error if using a probe with a 1M input resistance). However, the capacitive component can present low impedances to the circuit being measured, especially at frequencies greater than a few MHz. For example, a probe with a 20pF input capacitance will present an impedance of 400 ohms at 20 MHz or 80 ohms at 100 MHz. This is obviously much less than the resistive impedance and could attenuate the signal being measured. See Figure 1 below for a typical test setup. If Rsource is 100 ohms and Cprobe is 20 pF the source resistance and probe impedance will act as a low pass filter with a corner frequency of 80 MHz. This means that even if you are using a high bandwidth oscilloscope, the probe itself could limit your bandwidth and mask any high frequency behavior that you are trying to measure.

Figure 1. Typical Test Setup

Figure 1. Typical Test Setup

From the above explanation, it is clear that having an understanding of input capacitance is important when measuring high frequency signals. The next few sections will explain how one can measure this probe capacitance. We will measure the input capacitance of Aeroscope as a demonstration of this procedure.

One way to calculate the capacitance of an unknown load is to apply a step function and measure the rise time. The time constant Tau is equal to the product of the resistive and capacitive impedance elements. Tau is the time required for the voltage to rise from its initial value to 63% of its final value. Figure 1 above will be used to represent the test setup, Rload is not present and Tau is equal to (Rsource || Rprobe) * Cprobe. Use a value of Rsource that is large enough so that each pF of capacitance causes an observable delay in rise time. The value of Rsource we used for this test is 470k ohm. This gives a Tau of 0.45 us per pF, which is easily observable on an oscilloscope.

Once the test is setup, adjust the amplitude of the square wave source until the signal occupies the entire screen, see Figure 2 below. Since the scope screen is 8 divisions tall and we are looking for the point that the signal has risen by 63% we need to see how long it takes the signal to rise 5 divisions (5/8 = 62.5%).

Figure 2. Step response with amplitude equal to the full oscilloscope screen. Time scale = 5 us/division

Figure 2. Step response with amplitude equal to the full oscilloscope screen. Time scale = 5 us/division

The rise time is measured as shown in Figure 3 to be roughly 4.5 us.  The source resistor (470k) in parallel with the scope's input resistance (10M) gives an effective source resistance (Rse) of 449K (Rprobe || Rsource). The input capacitance can then be calculated to be (Tau/Rse) equal to 10 pF. This capacitive load is comparable or lower than most passive probes that come standard with 100 MHz bandwidth oscilloscopes.

Figure 3. Rise time measurement. Time scale = 1us/division

Figure 3. Rise time measurement. Time scale = 1us/division

A 10 pF input capacitance will present an impedance of 159 ohms at 100 MHz. This would cause .4 dB of attenuation with Rs of 50 ohms, or 1.5 dB of attenuation with Rs of 100 ohms.