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# Four-Terminal sensing

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#### juliog

##### Newbie level 6
Hi guys,

I was having a look at these questions about a four-wire measurement system and I'm not sure about the answers:

A four wire system is employed to measure a resistive load, Rx. The model for each electrode Zp is the parallel combination of a resistor Rp=1MΩ and a capacitor Cp=1nF. The system is being driven by a sinusoidal current of 1.sinωt [μA]

Which is the voltage amplitude of the output signal measured at 0,1kHz,1kHz, 10kHz, 100kHz and 1MHz?
Which is the voltage amplitude at the input as a function of the frequency?
Which is the best frequency to perform the measurements? Why?

They are simple questions but I feel really confused. Isn't the voltage amplitude at the output the same for all frequencies? Why some frequencies are better than others to perfrom the measurements?

Thanks!

there are caps in the system so it effects the freq response.

You should consider voltmeter as an open cct means no current flow through it (to accept other ways you need to know internal impedance of voltmeter, that increases computational complexity, skip here).
Then Voltage across to Rx would be (simple cct theory) U=Rx*Vi/(2*Zp+Rx) means Rx=2*Zp*U/(Vi-U), here Zp=R/(1+sRC) (R=1M, C=1n), then you should calculate using the actual values.
For the frequency question (third question) for me, consider parallel RC impedance (serial wires model), as frequency increases imp of capasitor decreases means total impedance of the RC network decreases. To be on the safe side impedance of the cap should be as small as possible compared to R, so higher freq signal is better more correct measurement (but it will depend also depend on the Rx).

Hope helps

juliog

### juliog

Points: 2
Thanks for ur help. As the system is driven by a current source, the voltage amplitude across Rx is always the same, isn't it? But the votage amplitude at input (Rx+2Zp) increases with lower frequencys. So i think you mean higher frequencies are "safer" to avoid an overdrive, right?

The first question seems a bit silly... The voltage amplitude at the ouput (across Rx) is always the same.

you are right, actually i missed that force is an current source, consider as voltage source, but the main idea is the same...
In this case, as you said, voltage across Rx is always is fix, voltage across the current source increases depending on RC network impedance which is dtermined by frequency.
A similar method is used to define earth/soil electrical charecteristic, hence there is no real current source, in that applicaiton, force source is an AC voltage source...

juliog

Points: 2