Complex numbers & impedance

What is the proper syntax to assign an impedance that is a complex number?

I have a circuit with an AC current source with an output of (in polar form) 16 45(degrees), connected in parallel to both a capacitor of impedance -j50 and an inductor of impedance j30. What is the proper way to label these elements in CircuitLab, and which simulation method should I use to find a solution? Do I have to use the current function generator element instead of the current source element?

If it is relevant, I am looking for a Norton Equivalent of the circuit. Thanks!

by tonypro17
November 04, 2013

To simulate this you can use a Time domain or a Frequency domain simulation.

However, to do this you need a complete description of your source.

16 45(degrees) is incomplete. It only defines two of the three parameters of amplitude, frequency and phase.

Without all three parameters it is not possible to fully describe the amplitude and phase of the currents and voltages in your circuit.

by signality
November 04, 2013

Oh, well the frequency is not listed, so I didn't have a number to give.

I guess my question could be a little simpler: does circuitlab work with phasor transformations? How do you create an element with impedance?

by tonypro17
November 04, 2013

You can't work directly with phasors in CL.

You can work with "physical" components: resistors, capacitors and inductors.

A resistor has a frequency and phase independent resistance.

A capacitor has a frequency dependent reactance:

X_C = 1/(ω*C) = 1/(2*pi*f*C)

An inductor has a frequency dependent reactance:

X_C = ω*L) = 2*pi*f*L

So, you have to know a frequency, f, at which the capacitor of impedance -j50 and inductor of impedance j30 are actually measured in order to define the actual capacitor C and inductor L values.

Then you can simply draw the circuit in CL assigning the appropriate R, C and L values.

A sinusoidal source can be defined in either the time or the frequency domain as an amplitude, a frequency and an initial phase.

There is little documentation about setting up time domain sources but there are many examples to play with. Note however that the phase of the function generator sources work backwards: to set a COSINE you need to set a phase of -90 degrees.

https://www.circuitlab.com/circuit/hvqear/sine-and-cosine-cl-sources-01/

Information about frequency domain sources is here:

https://www.circuitlab.com/docs/the-basics/#frequency_domain_simulation

I don't think it is clear from the Documentation how to use this feature. An example of how to use it is given in this thread:

https://www.circuitlab.com/forums/support/topic/52d2y9zd/ac-circuit-analysis-not-giving-expected-answer/

Note that in the time domain, the amplitude is the peak to peak value whereas in the frequency domain the amplitude is in effect relative to whatever you define as being your reference signal. So if you think of your reference as being aV RMS then all the signal levels are referenced to this aV RMS.

I'm not sure if this answers your question but hopefully it will point you in the right direction.

:)

by signality
November 05, 2013

This helps quite a bit, thanks!

by tonypro17
November 05, 2013

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