September 1, 1997

Simple technique measures small capacitance

Rich Kochis and Joe Eccher, Hewlett-Packard, Greeley, CO

A simple technique (Figure 1) can measure small capacitance, such as the capacitance of a scope probe (Figure 3a), a 10-pF capacitor (Figure 3b), and a pc-board trace (Figure 3c). The idea is to use a ramp generator and an oscilloscope (Figure 1a) to measure the delay in the ramp that corresponds to the capacitance. Equations provide the best explanation of how the tech-

nique works. For the circuit in Figure 1b, which dri ves channel 2 of the oscilloscope,

Thus,

V_IN is a ramp, so

(1)

and

Therefore,

and

For T>>RC,

(2)

and V_IN(t) and V_OUT(t) become two parallel lines (Figure 2).

From Equation 1,

and from Equation 2,

Thus,

You can define DT as

For the voltage at which V_IN(T₁)=V_OUT(T₂) and when T>>RC,

Thus,

where

Therefore, C depends only on DT and R (when T>>RC), and C is independent of the slope, K, and voltage level. To measure T, you must only make sure that the voltage slopes are parallel, which is the case when T>>RC. The oscilloscope's capacitance is included in the reference-voltage measurement of T₁. Therefore, the unknown capacitance is the variable in the measurement of T₂ divided by R. (Note that if the unknown C measurement includes an input to an IC, you need to limit the input ramp voltage to less than 0.5V.) (DI #2075)

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