EDITOR’S NOTE:

The above equation has several errors.

1. a voltage cannot equal a voltage squared, so \(V \neq <(V)^2>\) and \(V_{mult} \neq <(V_J + V_{\textrm{other noise}})^2>\)

2. YOu should write \(<(V_J)^2> + <(V_{other})^2\)>, not \(<(V_J + V_{\textrm{other noise}})^2>\). There are two independent (random) noise sources — the resistor being measured (Johns) and the amplifier circuits (instrumentation) —so you don’t add their voltages \(V_{Johnson}\) and \(V_{instrumentation}\), you need to add \(<(V_{\textrm{Johnson Noise}})^2>\) and \(<(V_{\textrm{instrument noise}})^2>\). See textbook and manual.

3. if \(V_{Mult}\) means the multiplication of two voltage signals \(V_s \times V_s\) , it should be written \(V^2_{mult}\)

4. if \(V_{Mult}\) means the voltage signal measured by a multimeter, then it should read \(V^2_{multimeter}\) = \((V_s \times V_s) / (10 \ V)\) since the output of the multiplier is divided by a 10 V reference signal before being sent to the multimeter

A better set of equations would be

\[<(V_{\textrm{total noise}})^2> = <(V_{\textrm{Johnson Noise}})^2> + <(V_{\textrm{instrument noise}})^2>\]

and

\[V_{\textrm{multimeter}} = \frac{<(V_{\textrm{total noise}})^2> }{\textrm{10 V}} = \frac{ <(V_{\textrm{Johnson Noise}})^2> + <(V_{\textrm{instrument noise}})^2>}{\textrm{10 V}}\]