Resistances Affect Voltage Measurements

Suppose you want to measure the voltage in a circuit that has an impedance of, say, 1 Mohm. ?If you connect this signal to a handheld DVM, such as a Wavetek 25XT DVM that has an input impedance of 10 Mohms, the instrument's internal resistance will affect the voltage measured, as shown in the figure. Use the ratio of the DVM's resistance to the total resistance to determine the voltage you see on the meter.

Vmeter = Vunknown * [Rmeter / (Rmeter + Rsensor)]

I put a 1.04 Mohm resistor in series with a power supply and measured the voltage across the supply output (1.96V) and then with the DVM in series (1.75V). That's about a 10-percent error. When I ran the test with an HP 3478A digital multimeter, which has a 10¹⁰-ohm input resistance, the reading from the power supply (1.905V) matched the reading from the power supply with the resistor in series. To reduce this type of error, Keithley Instruments recommends a measurement instrument have an input resistance at least 100 times the resistance of the voltage source.

Most high-quality DVM and source-measure units have an input resistance of 10⁹ or more ohms. Oscilloscopes have input resistances of 1 Mohm. Unfortunately, specs for some plug-in data-acquisition boards and USB-plug-in modules lack this information. Ask before you buy.

You also must include all shunt resistances when you consider a meter's input resistance. These resistances can arise from leakage in test leads, dirty connectors and contacts, closely spaced conductors, and even solder-flux residue on a circuit board, which is particularly a problem on prototype PCBs. Many manufacturers of instrument cables do not provide a cable-leakage specification except for radio-frequency signals.

Voltage-measuring instruments also have a small bias current that flows in or out due to the nature of internal circuits. This bias current flows through the circuit you want to test and causes a small voltage error. The Keithley 2182A nanovoltmeter, for example, specifies a bias current below 60 pA for -10 to +5V and 120 pA for 5 to 10V. You can use Ohm's law to calculate the voltage that can add to or subtract from the voltage you want to measure. If you still have a 1 Mohm resistance in your circuit, the 60 pA bias current can cause an error of 60 µV. For a 2V signal, that might seem minor, but keep in mind that offset remains constant across a voltage range, so the error becomes more noticeable on lower-voltage meter readings.