1
\$\begingroup\$

This circuit here.

I get the overall formula, I'm not sure what to do about the 1 mF and the 1000 μH. Do I convert them in some way or ignore them?

What if I'm trying to find total power dissipated or voltage across this circuit from a current?

\$\endgroup\$

3 Answers 3

2
\$\begingroup\$

This circuit looks spooky at first glance but it is actually three paralleled impedances. The below simulation shows the circuit when properly redrawn:

enter image description here

When simulated, it shows an impedance mostly ohmic and of flat magnitude across frequency:

enter image description here

To analyze this network symbolically, you can use the brute-force analysis or the fast analytical circuits techniques abbreviated FACTs as described in my last book. This is a second-order circuit (two poles then) and I can infer from the arrangement that there are also two zeroes. The general form of this transfer function is simply:

\$Z_{in}(s)=R_0\frac{N(s)}{D(s)}\$

The dc resistance is immediate: place all energy-storing elements in dc (short the inductor and open-circuit the capacitor) and determine the resistance by inspection:

enter image description here

This is the first part of the FACTs analysis and I leave the rest to you. The brute-force analysis given below:

enter image description here

Sunday morning edit:

I have spent a few minutes to extract the complete transfer function and it is given below. The complete TF was obtained by inspection only - no equation or complicated manipulations - and tested against the brute-force version that I did not purposely expand. Both answers are rigorously identical.

enter image description here

\$\endgroup\$
2
  • \$\begingroup\$ Did you use Mathcad to generate those graphs in the last two figures? \$\endgroup\$ Jan 30, 2022 at 7:36
  • 1
    \$\begingroup\$ The upper one is with obtained with a SPICE simulator (ICAPS) while the other ones yes, with Mathcad. \$\endgroup\$ Jan 30, 2022 at 8:10
1
\$\begingroup\$

Unclear. In the simplest case of DC resistance, you substitute inductors by shorts and capacitors by open circuits.

Regarding total power and voltage, again, it depends how the circuit is being excited: DC, harmonic AC, square wave, etc.

\$\endgroup\$
2
  • \$\begingroup\$ How would you calculate it if it was DC? \$\endgroup\$
    – Adam X
    Jan 29, 2022 at 10:16
  • \$\begingroup\$ Find the DC equivalent resistance and then proceed as normal \$\endgroup\$ Jan 29, 2022 at 10:20
-1
\$\begingroup\$

This can be easily understood by basic circuit theory concepts. Impedance of inductor with inductance L is given by jwL, where w is angular frequency of source. Similarly, for impedance of capacitance C is given by 1/(jwC). Now replacing these values in circuit, we can easily simplify the circuit as follows.

R2 and inductance L are in series, giving equivalent of W=(10k+j0.001w). Similarly, R5 and R6 are in series, giving X=0.02MOhm. Now R3 and capacitance are in parallel, giving equivalent of Y=j11w/(1+j11w). Now Y is in series with R4 giving Z=Y+9kOhm.

Finally W,X and Z are in parallel, whose equivalent could be easily calculated. Exact value of impedance can be calculated by substituting w.

Thanks

\$\endgroup\$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.