Impedance mismatch

Question

When I connect an oscilloscope to a function generator use both oscilloscope cable (one connect to the scope and one connect to the FG), I got 700mVpp when outputing a sine wave of 1Vpp and 10kHz.

But when I use the BNC cable connects to the FG, and the scope cable connect to the scope I got 2Vpp output with the same input.

What is the exact calculation behind this?

Answer 1

If you're saying that the open-circuit output of the function generator is 1VPP and that when you connect it to the scope the scope reads 700mVPP, then if your scope's input impedance looks like 10 megohms paralleled by some few picofarads:

EDIT: 1 megohm paralleled by some few picofarads:

the generator impedance looks like 428k ohms, so clearly something's very wrong.

Do you have your scope's impedance set at 50 ohms, perhaps, and with half of 1VRMS coming from a 50 ohm function generator you're reading 0.7V peak from the scope?

Answer 2

What you might be seeing is Root Mean Square, which is calculated as the amplitude \$a\$ over the square root of 2:

$$\frac{a}{\sqrt2}$$

For amplitude values of 1, this works out to ~0.707.

Check the settings on your scope; perhaps it is showing you a measured RMS value instead of peak to peak? (As in, a text value, rather than what's displayed on the grid. My scope can show various measured values aside from the normal waveform grid view.)

Answer 3

You say you are outputting 1VPP, and I assume when you say you're "seeing" 700mV on the scope that you are also speaking of PP. If that is the case then there is no calculation to it. Either the FG or the scope is simply out of calibration.

Answer 4

Just to add to what JYelton said, read more about RMS values, but the \${\sqrt2}\$ factor is generally only applicable to sine waves (might be others too, have to do the math). For example, a square wave would have RMS value equal to its Peak.