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I am using an electronic load to draw current into my DUT. I have set Vin to a voltage within the E5061B maximum bias levels, but when I draw current the voltage drops. Why is this happening?

The output impedance of the DC bias source is 50 ohm (nominal).

A voltage drop will appear across this impedance as current flows through it in accordance with Ohm’s Law (Voltage = Current * Resistance).

For example, a 0.5 V drop would appear if the load were to draw 10 mA of current through the output.