# Multi Frequency Circuits

Discussion in 'General Electronics Chat' started by sjgallagher2, Oct 1, 2013.

1. ### sjgallagher2 Thread Starter Active Member

Feb 6, 2013
128
12
How would I go about analyzing this circuit?

Where the top AC source has a frequency of 10Hz, and the bottom source has a frequency of 50Hz. I can't say I've come across something like this before so I'm a bit confused. In my mind I'd start going around the circuit and attempt to analyze, but the multiple frequencies never came into account before so now I don't even know where to start. Penny for your thoughts?

2. ### Nykolas Active Member

Aug 27, 2013
112
36
You need to clarify some things:

- Output impedances of the gens: equal or not?
- Measurement point: which end of the resistor or differential?
- Signal amplitudes: Equal or not?

E

3. ### ScottWang Moderator

Aug 23, 2012
6,589
1,021
What is this circuit used for?
It looks like that two AC source will fighting?
Are you trying to modulating two AC source?

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4. ### sjgallagher2 Thread Starter Active Member

Feb 6, 2013
128
12
In a way, I am, but this specific circuit isn't going to be used for anything. It's just something I whipped up to understand what happens when two ac sources with different frequencies are applied to the same linear component. Eventually, that'll lead to understanding nonlinear components hopefully and with that the process of mixing! I'm still learning and I don't quite understand the big concepts of mixing. I understand mathematically what's going on, but I don't understand how someone took those mathematical concepts and used them with electrical/electronic components. Forgive me if I'm a bit misguided

5. ### sjgallagher2 Thread Starter Active Member

Feb 6, 2013
128
12
And I'm measuring the voltage across the resistor

6. ### Veracohr Distinguished Member

Jan 3, 2011
670
101
1. Pick a place to start - like the left side of the upper voltage source.
2. Apply KVL: Go around the loop adding and subtracting voltages as necessary, and sum around the loop equals 0. Add the negative-to-positive source, subtract the voltage drop across the resistor, subtract the positive-to-negative source. Solve for the voltage across the resistor.

7. ### ScottWang Moderator

Aug 23, 2012
6,589
1,021
See the waveform below and google "op amp subtractor circuit".

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8. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
790
I've attached a Labview Simulation of the input and resulting difference waveforms along with the resulting waveform spectrum. As expected no inter-modulation / mixing (multiplication) results and the output spectrum contains terms only in the input signals (10 & 50 Hz).

Interestingly it's worth noting the result would be essentially the same irrespective of whether one is adding or subtracting the two waveforms. Over a suitable time frame the effective RMS value of the summed or differenced results would be the same.

If one replaces the subtraction function with a multiplication function then inter-modulation products appear in the output waveform spectrum.

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9. ### ScottWang Moderator

Aug 23, 2012
6,589
1,021
That's what I'm asking - Are you trying to modulating two AC source?

We have a case using three waveforms to do the modulation.

10. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
790
This probably relates to the OP's other (unanswered) earlier thread ...