Power equations for transformer, impedance matching

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antknee

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I have the following set up: Audio amp --> audio transformer --> piezo

I'm trying to understand just how much power I need. The amp has a big gain bandwidth and i get a decent signal for the frequencies I need ~100KHz. With the mains power this is what I get:

Input into amp 1Vpp @100KHz : output of amp 10Vpp : input into transformer primary 3.2 ohms, 10Vpp : output of transformer 1.2Kohms, 180Vpp : Piezo 180Vpp impedance 100 ohms.

Now: Power =(V x V)/R

So if I do the sums (90 x 90)/100 =80 Watts.

Its that bit I don't get, I clearly don't have 80W on the piezo. So there is some impedance matching that I don't quite get. How do I calculate how many watts I really have on the piezo?

Thanks.
 
Where do you get the 100 ohms from? (and it's not 90V RMS feeding it either).

The input to the transformer (assuming 3.2 ohms) is only 3.8W - power to the piezo will be slightly less than that.
 
180Vpp is ~64Vrms. Assuming that the impedance of the Piezo is resistive (big assumption), the power into the Piezo would be 64^2/100 =40W, which doesn't make sense.
 
Last edited:
First, convert to RMS (.707 x Peak) or 63.63 volts.
Divide by the total resistance (1.3k)= 3.1 watts in the output circuit. You can check this by calculating the current in the secondary circuit and then multiplying by the voltage across the piezoelectric device and get 3.11 watts again (I rounded off).
 
The piezo is listed on the website were I bought it at 100 ohms impedance. It could be wrong but I have no way of checking. The piezo is capacitive, it has a shunt/static capacitance of around 2nF.

So it looks like I use the input power in the primary transformer ~ 3.8W and essentially I have a little less than this on the piezo.

The measured volts are right at 180Vpp so assuming V~ 64Vrms:

R= (64x64)/3.8 = 1.07 Kohms.

Hmmm. That impdeance looks out by a lot bigger factor than I'd imagine.
 
Remember, you specified 1.2K in the secondary that has to be accounted for as well as the 0.1k in the device. That is where I get the 1.3k total I used for the calculation.
 
With 3.1W

R= (64x64)/3.1 = 1.3K

The 1.3K is 100 ohms piezo and 1.2K secondary transformer coil.

I didn't know I'd have to include the secodary transformer coil impedance. Thanks all.
 
Since the OP talks about p-p then maybe the signal is a square-wave and not a sine-wave measured in RMS.

The transformer has an impedance of 3.2 ohms only when it is loaded with 1.2k ohms which it does not have.
An audio transformer (for a PA speaker in a store?) will not work properly at 100kHz anyway.
If the transformer is perfect (ha, ha it isn't) then it will stepup the voltage only 19.3 times to 193V p-p.
 
antknee said:
The 1.3K is 100 ohms piezo and 1.2K secondary transformer coil.

I didn't know I'd have to include the secodary transformer coil impedance. Thanks all.
Click to expand...
The secondary transformer impedance is just the reflected impedance from the primary 3.2 ohms based on the turns ratio. It actually proportional to the amplifier output impedance, which is likely much less than 3.2 ohms, so the secondary impedance will also be less (this neglects the transformer dc resistance which is usually significantly less than the impedance ratings).
 

I know what you are saying is right, but I don't quite understand. The amp is best matched for impedance output at 4 ohms and pretty happy at 8 ohms and the 3.2 ohms I am actually using. The transformer loses around 10% which is I think normal.

@audioguru. The transformer outputs a perfect sine wave at 100KHz and anything above around 200Vpp cracks the piezo. It actually doesn't matter whether I input a square or sine wave from an output point of view because the piezo will round it off to a sine wave regardless, so I always input sine.
 
Old fashioned vacuum tube (valve) amplifiers matched their fairly high output impedance to the speaker impedance with an output transformer.
Modern solid state amplifiers are made to drive 4 ohm and 8 ohm speakers but the output impedance of the amplifier is 0.04 ohms or less for good damping of the resonances of speakers.

Since you have 180V p-p sine-wave output (64V RMS) then the transformer is loaded with about 1k to 1.2k ohms.
The power from the amplifier is 3.9W into 3.2 ohms, if the transformer has a 1.2k ohm load.
 
audioguru said:
Since you have 180V p-p sine-wave output (64V RMS) then the transformer is loaded with about 1k to 1.2k ohms.
The power from the amplifier is 3.9W into 3.2 ohms, if the transformer has a 1.2k ohm load.
Click to expand...

So how much power would you estimate is on the piezo?
 
A half decent transformer passes at least 90% of its input power to the output load. Then the piezo gets 3.5W.
 
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