# Matching impedances for maximum power

Discussion in 'General Electronics Chat' started by JStitzlein, Mar 5, 2011.

1. ### JStitzlein Thread Starter Member

Dec 6, 2010
53
0
I'm trying to calculate the maximum power transfer theorem for this filter that is in the worksheet.

"The problem is that an L-C filter has a input impedance and an output impedance which must be matched. The voltage source impedance must match the input impedance of the filter, and the filter output impedance must be matched by rload for a flat response. The input and output impedance is given by the square root of (L/C)."
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Looking at just matching the source impedance to the input impedance of the filter, I spiced the circuit and left out the load impedance of 316ohms.

I believe this should be matched for equal power, but my power calculation is off by three orders of magnitude.

My approach is not right and i'm not sure why.

2. ### JStitzlein Thread Starter Member

Dec 6, 2010
53
0
Doh! I just realized that power is not calculated in the same way like a resistor. I'm going to read the power factor section and try this calculation again.

3. ### The Electrician AAC Fanatic!

Oct 9, 2007
2,397
355
Try doing the calculations at about 500 Hz instead of 1 Hz.

4. ### JStitzlein Thread Starter Member

Dec 6, 2010
53
0
Would it matter if the calculation is done at a different frequency?

I realized why my answers were wrong, it's because i made a simple mistake and ignored the fact that my calculation had to be for a series current and series load resistance. What I was doing was using L2's split current, and L2s impedance and calculating power across that.

How do you calculate the impedance for the LC network?

5. ### JStitzlein Thread Starter Member

Dec 6, 2010
53
0
Can someone point in the right direction for calculating impedances of L&C? Is this the same thing as a transfer function?

6. ### The Electrician AAC Fanatic!

Oct 9, 2007
2,397
355
The "impedance" of a tee network like this can be considered to be the image impedance (http://en.wikipedia.org/wiki/Image_impedance).

For a low pass tee like this the image impedance in the pass band is real and is imaginary in the stop band. The image impedance at low frequencies well below the corner frequency is about 447 ohms. At 503 Hz, the image impedance is about 316 ohms.

But, these numbers don't imply that the impedances driving and loading the tee should be equal to the image frequency at a given frequency if that frequency is in the pass band.

If you'll solve for the input impedance to the tee network when an arbitrary RL is connected to the output, you'll find that below the corner frequency the input impedance is essentially the same as RL. So, for maximum power transfer (in the pass band) with a low pass, symmetrical, lossless tee network like this, just connect a load RL equal to Rg.

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