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Measuring complex Z

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joeh100

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How to measure complex Z?

Can someone describe a method of measuring complex Z. For example: what is the input and output Z (@ 10MHz) for the attached amplifier.

Thanks,

Joe
 

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Here is how I would do it: Look at my modified version of your circuit. The input impedance Zin = V(in)/I(R6). I pulled R6 out of the generator to have a place to monitor the input current.

When you do a .AC analysis, this expression V(in)/I(R6) is complex. You can plot the expression as a complex variable, or plot the Re() and Im() parts separately. You can do the same thing for the output impedance. Note I put a 1mΩ resistor R7 to have a place to get the output current. I suppose I could have used I(C3) instead... Convert the plots to "cartesian" instead of "Bode"

Similar methods can be applied to get power gain, transferimpedance, etc, etc. This is why I love LTSpice; you can do anything you want to with it. Great tool.
 

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OK, so I'm a little confused by complex impedance. What's going on when the real part goes negative?
 
The current flows the other way
 
Hi,

The current though R6 might be negative, so it might be necessary to change from using i(R6) to -i(R6) to get the right results.
Try it with a 1 ohm resistor first rather than an entire amplifier, then a cap in series with a resistor, then an inductor in series with a resistor, see if they show the correct results of both real and imag parts. The 1 ohm resistor tested alone should of course show a +1 ohm real part and zero imaginary part not a -1 ohm negative real part.
If the real part goes negative really then that means it's a negative resistance.

We might see a negative resistance show up, but im not convinced yet that it should be so. I guess it could be a property of the input of this amp but it must be because of that inductor somehow feeding back through the transistor at some frequencies. I think it deserves more attention.
 
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More info: Look at the first sim of the passive network. Note R6. When creating the schematic with the LTSpice graphics editor, R6 can be installed either way around, meaning that this defines which way current flows through it when data is saved when the simulation runs. This applies to all symmetric two terminal components, like resistors, capacitors, inductors, etc.

It is simple to tell which way around any given component is instantiated, but only after the Sim has been run. Moving the cursor over the component shows a miniature "Amprobe", where the current direction is shown with an arrow.

I plot Zin = V(in)/I(R6) in the top plot pane. With R6 oriented so that current flows through it from left to right, then everything makes sense, including the Real and Imaginary plots. If R6 was flipped left to right, then Zin = V(in)/-I(R6), and all the plots are effected appropriately. The blue text is from the LTSpice help file, and defines what waveform arithmetic functions are specific to complex waveforms.

Now back to the OP's Amp. I had to turn R6 around, and widen out the frequency range to get these plots. Note that I(R6) reverses and V(in) is higher than the input source for a range of frequencies. This shows that the amplifier is feeding back into its input, exhibiting some signs of instability. It shouldn't be surprising then that the input impedance goes negative...

Remember the "Q-multiplier"?
 

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Hi again,


Yes these 'polarized' resistors always cracked me up :)

In the circuit that was posted it looked wrong so i thought i would mention it. Either way makes it work so that should be fine i think.

I havent investigated the negative resistance phenomenon yet maybe you did.
 
... This shows that the amplifier is feeding back into its input, exhibiting some signs of instability. It shouldn't be surprising then that the input impedance goes negative...

Remember the "Q-multiplier"?
 
I have simulated the input impedance with PSpice using simply an ac CURRENT source of 1A.
Thus, the input voltage is identical to the input impedance (kV=kOhms)
Results are enclosed.

The peak is at approx. 3 MHz.
 

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