Hi all,

I'm having a problem with the calculation of the negative transresistance in question 9 on the page http://www.allaboutcircuits.com/worksheets/switch_c.html. I was able to calculate all the other equivalent resistances, but since my same methods don't work on case E, I'm looking for someone who can really explain to me what is the best way to calculate these resistances.

Thanks in advance to everyone who gives it a try

 

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Dave

 

It's been a while already because I've been working on other things than switched capacitors, but I'm still curious about this negative transresistance.

I try to solve it as follows: I define two voltages, V2 on the left side and V1 on the right, and assume V2 > V1.
In the beginning, assume that the left side of the capacitor is connected to V2 and the right side to ground. When the left side is switched to ground, the voltage at the right side is -V2 (this is just a change of reference). Now the right side is connected to V1. So the voltage at the right terminal changes from -V2 to V1. This requires a current to flow from the V1 terminal into the capacitor, or a charge transfer of C(V1+V2).
Another way of viewing this is purely looking at the capacitor charge: in the beginning, this is CV2. After the first switch, the charge becomes -CV1. The charge transfer is again:

deltaQ1 = CV2 - (-CV1) = (V2+V1) C

Or you could also say that there was a net charge transfer from the left side to the right side of:

deltaQ1 = ( (V2-0) - (0-V1) ) C = (V2+V1) C

This process repeats in the other direction, resulting in a second charge transfer:

deltaQ2 = ( (0-V2) - (V1-0) ) C = -(V2+V1) C


Either way, I'm going to have a problem with the fact that the voltages are summed in these formulas, while I'm applying a differential voltage V2-V1. In all the other cases, you can just divide out the voltages and end up with a nice equivalent resistance formula.

While I don't really need to use the negative transresistance, I have a long term project in which I need to model parasitic switched capacitor effects and I'm too curious to just accept a formula like this without knowing how to calculate it. Hope you can help me out here