Low Level Measurements Handbook

this input capacitance consists of the meter input capacitance in parallelwith the input cable capacitance. Even a small amount of shunt capacitancecan result in long settling times if the source resistance is high. For example,a shunt capacitance of 100pF (including the input cable) and a sourceresistance of 20GΩ will result in an RC time constant of two seconds. Tenseconds must be allowed for the measurement to settle to within 1% of thefinal value.Figure 2-7 demonstrates the effects of shunt capacitance loading on theinput of a typical high impedance voltmeter. The signal source is representedby V S and R S , the shunt capacitance is C SHUNT , and the measured voltageis V M . Initially, the switch is open, and C SHUNT holds zero charge.When the switch is closed, the source voltage (V S ) is applied to theinput, but the measured voltage across C SHUNT doesn’t rise instantaneouslyto its final value. Instead, the voltage rises exponentially as follows:V M = V S (1 – e t/RSCSHUNT )Also, the charge (Q IN ) transferred to the capacitor is:Q IN = V S C SHUNTThe charging of C SHUNT yields the familiar exponential curve shown inFigure 2-8. After one time constant (τ = RC), the measured voltage rises towithin 63% of its final value; final values for various time constants are summarizedin Table 2-1.FIGURE 2-8: Exponential Response of Voltage Across Shunt Capacitance10090807063 6050Percent of 40Final Value 30(V S ) 20100Time0 1.0 2.0 3.0 4.0 5.0R S C SHUNTTABLE 2-1: Settling Times to Percent of Final ValueTime Constant (τ*) Percent of Final Value1 63 %2 86 %3 95 %4 98 %5 99.3 %*τ = RC, where R = resistance (ohms), C = capacitance (farads)Measurements from High Resistance Sources 2-9