Altifigence Academy

7 / 32 · Concept

Loading changes what you measure

Calculate meter and amplifier input loading instead of assuming infinite impedance.

Every connected input is a load

A voltmeter or amplifier input has finite impedance. Connecting it creates a branch, and a branch changes KCL. Model the source by a Thevenin voltage and series resistance, then model the input by resistance to ground for this DC calculation. At higher frequency, input capacitance also matters; a quoted DC resistance alone cannot predict a fast waveform.

Suppose a sensor produces an open-circuit 1 V and has 100 kΩ source resistance. A 1 MΩ meter reads 1×1000/(100+1000)=0.9090911\times1000/(100+1000)=0.909091 V. The approximately 9.09% error is caused by the measurement connection, even if the meter itself is perfectly calibrated. A 10 MΩ input reads 0.990099 V, about 0.99% low.

Specify the error budget

For a resistive load, fractional droop relative to open circuit is RS/(RS+RL)R_S/(R_S+R_L). To keep this below 1%, require RL>99RSR_L>99R_S. Equality gives exactly 1%. A common “ten times larger” rule gives approximately 9.09% droop, so it is inadequate when the requirement is 1%.

An amplifier can isolate a source if its input resistance is sufficiently high and its output can drive the next stage. Its input bias current introduces another voltage error through source resistance. For example, 10 nA flowing through 100 kΩ gives 1 mV. Bias current, input resistance, and input capacitance are separate effects; one favorable specification does not remove the others.

Make a diagnostic comparison

Predict a measurement with the input connected and disconnected. If a high-impedance sensor looks correct with one instrument but low with another, compare instrument impedance before replacing the sensor. Document the actual probe or meter mode because selectable modes can use different impedance. Keep measurement leads short for later AC work, and record the ground connection. The circuit being measured includes your instrument, not just the components drawn on the original page.

For a low-impedance 100 Ω source driving 1 MΩ, the droop is only approximately 0.01%; this tells you when loading can reasonably be neglected rather than treating all measurements as equally invasive.

Try it yourself

A 2 V source with RS = 20 kΩ drives a 100 kΩ input. What voltage arrives?

Read the explanation

V = 2 × 100/(20+100) = 1.666667 V. The droop is 16.6667%. A 2 MΩ input would reduce droop to about 0.9901%.

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