Voltage amplification of 1kHz wave with transformer

[maelh]

I am feeding a 1kHz sine wave with a 2Vpp amplitude into a transformer (secondary), which shows as 16.2Vpp sine on the transformer primary.

The sine wave from the signal generator is terminated with a 50 ohm resistor (exactly 46.33 Ohm).
The transformer secondary is 5.469mH and the primary is 618.5mH, both measured with an LCR meter.

The transformer is tapped (3 terminals), so I additionally measured left to middle terminal (163.29mH) and middle to right terminal (163.33mH).

Assuming:
transformer ratio TR = N1/N2 = V1/V2  or  V1 = TR * V2 (where 1 is primary, and 2 secondary, N number of turns, V voltage).
and
L1/L2 = (N1/N2)^2 = TR^2 (where L1 and L2 are the inductance of the primary and secondary coil, respectively).

With the measurements above I get TR^2= L1/L2 => TR = sqrt(L1/L2) = sqrt(618.5/5.469)=10.6345
and
V1 = 10.6345 * V2

So given the 2Vpp input, I would assume an output of about 21.27Vpp, but I get 16.2Vpp, which seems quite a big difference.

Edit (the transformer "input" signal is not the 2Vpp the sig gen outputs):
When I view the output of the sig gen with the approx 50 ohm resistor across the signal and ground pins, the scope will only see a sine wave of about 1.50Vpp at the transformer "input" (secondary coil). So that in theory I should get 15.95Vpp approximately at the output (primary coil), which is closer to the 16.2Vpp which the scope shows in real.

So my remaining questions are:
Is my logic so far correct? (Especially how I determined TR based on the coils' inductances).
Why does the signal from the sig gen have such a significant difference from the expected 2Vpp output, when terminated with the approx 50 Ohms?
Shouldn't the transformer output be lower than the theoretically computed value, due to losses? Why is it slightly higher?

Edit2:
When increasing the frequency, the output signal (at the transformer primary) increases continuously until reaching 12kHz where it stabilizes to 20.4V approximately. Why is that?

[Zero999]

How are you measuring the voltages? 1.5V is close to the RMS voltage of 2V peak.

The reason the voltage increases, at a higher frequency, could be because it's getting close to the resonant frequency of the secondary coil, so it's acting like a poor man's Tesla coil.

[maelh]

I am measuring it with the Vpp entry of my scope. When connecting the sig gen to the scope with a bnc cable and a 50 ohm resistance in series, it shows approx the right voltage. So the measurement part should be fine.

Edit:
When leading the signal from the sig gen to the breadboard and terminating it with a 50 ohm resistor, it measures fine with the scope, too. But when I connect the transformer as well, the voltage of the sign gen, drops to approx 1.6Vpp.

[CaptDon]

Turns ratio of unknown transformers is usually more accurately measured when driving the winding which has the highest number of turns. So you have to play around a bit to figure out which winding that is and then go from there. Case in point, a 120vac input transformer with a very high current 2.5vac / 5vac secondary will always give wrong answers if you drive the secondary and measure primary for your calculations. The transformer is also best measured near its intended operating frequency. You wouldn't normally measure a power transformer at 1khz because the losses would make measurements meaningless.

[maelh]

The transformer is from a electronics experimenter kit, and meant to be attached to a speaker, so I assume it should work within the audio frequency range.

Also, shouldn't the measured inductances of a the centre tapped primary coils add up to the entire coil? The measurements shows something else, though: 163.29mH + 163.33mH <> 618.5mH

[fourfathom]

Also, shouldn't the measured inductances of a the centre tapped primary coils add up to the entire coil? The measurements shows something else, though: 163.29mH + 163.33mH <> 618.5mH

No, that measurement is close to what you should expect.  The inductance of a coil is a function of turns², so if the inductance of half the coil is 163mH, the full coil (with twice the turns) will be 163 * 2², or 652mH.  With parasitics, measurement errors, etc, the measured 618mH is fairly reasonable.

[Zero999]

The transformer is probably only telephone quality, with a bandwidth of 300Hz to 3kHz.

As mentioned above, the inducatances don't add, because they're coupled. If they were separate, coils, then the total inductance would be equal to the sum, but the coupling increases it. The two windings have the same inductance and number of turns, so doubling the number of turns will quadruple the inductance, which is close to what your measurments show. Look at the formula for calculating the inductance from the number of turns on a coil. Note the N², term, where N is the number of turns.
https://www.allaboutcircuits.com/tools/coil-inductance-calculator/

[Benta]

"The sine wave from the signal generator is terminated with a 50 ohm resistor (exactly 46.33 Ohm)."

What exactly do you mean by this? Have you placed a 50 ohm resistor across the output of the SG?

[maelh]

"The sine wave from the signal generator is terminated with a 50 ohm resistor (exactly 46.33 Ohm)."

What exactly do you mean by this? Have you placed a 50 ohm resistor across the output of the SG?

Yes.

[maelh]

No, that measurement is close to what you should expect.  The inductance of a coil is a function of turns², so if the inductance of half the coil is 163mH, the full coil (with twice the turns) will be 163 * 2², or 652mH.  With parasitics, measurement errors, etc, the measured 618mH is fairly reasonable.

Maybe it's also how the transformer is built, and there is a gap between the coils that creates less coupling than expected.
I don't think there can be much measuring errors, as I get quite consistent values and use an LCR meter with kelvin probes.

[Benta]

"The sine wave from the signal generator is terminated with a 50 ohm resistor (exactly 46.33 Ohm)."

What exactly do you mean by this? Have you placed a 50 ohm resistor across the output of the SG?

Yes.

Please don't do this, there's no reason for it. You're (over)loading the SG output for no reason. What you're making is an AC voltage measurement, where impedance matching is not needed. I suspect that your strange results come from this.

[fourfathom]

No, that measurement is close to what you should expect.  The inductance of a coil is a function of turns², so if the inductance of half the coil is 163mH, the full coil (with twice the turns) will be 163 * 2², or 652mH.  With parasitics, measurement errors, etc, the measured 618mH is fairly reasonable.

Maybe it's also how the transformer is built, and there is a gap between the coils that creates less coupling than expected.
I don't think there can be much measuring errors, as I get quite consistent values and use an LCR meter with kelvin probes.

Yes, I lumped "gap" into the parasitics category.  N² is accurate when there is tight coupling in the coil.  As you separate coil sections the coupling diminishes and the ² becomes something smaller.  But also realize that your measured inductance will vary as the measurement frequency changes, and the effect of the parasitics can also change over frequency.

[maelh]

Please don't do this, there's no reason for it. You're (over)loading the SG output for no reason. What you're making is an AC voltage measurement, where impedance matching is not needed. I suspect that your strange results come from this.

The reason for impedance matching was to get the same signal level (voltage) as the sig gen states, which works, using the resistor and no other load, except for the minimal one from the scope measuring the signal. When the sig gen gets overloaded, it will shut off the channel on its own (which it does not).

But yes, I tried already without a resistor, that's how I actually started. But then I get a way too high voltage of 25.4Vpp (at 1kHz). From theory, the result should be 21.27Vpp as mentioned in the first post.

Edit: When increasing the frequency (without the resistor), the peak is at 20kHz with roughly 37Vpp, and goes down again as I increase the frequency further.
All values that don't really follow from the calculations in the first post.

Are such larger variances normal? If so how would you use a transformer "reliably"?

[fourfathom]

Are such larger variances normal? If so how would you use a transformer "reliably"?

You will generally provide a load impedance at the *output* of a transformer.  The input impedance will be approximately the load impedance multiplied by the square of the in:out turns ratio. 

So, say you have a transformer with 100 turns on the input winding, and 300 turns on the output winding.  This is a 1:3 turns ratio, and will provide a 1:9 impedance step-up (and a 1:3 voltage step-up).  To present a 50-Ohm load to the signal source, you need to load the output winding with 450 Ohms.  Of course this only works when the transformer is designed for the appropriate impedances and frequency range.  In practice you also have to consider transformer resistive and core losses, leakage inductance, and various parasitic capacitances (and no doubt other factors that are above my pay grade).

[radiolistener]

I am feeding a 1kHz sine wave with a 2Vpp amplitude

What did you mean "2Vpp" amplitude? 

Vpp  = means peak-to-peak voltage
Vpk  = means amplitude voltage
Vrms = means rms voltage

Vpp = 2 * Vpk
Vpk = Vpp / 2

for sine wave:

Vpk = Vrms * sqrt(2)

As I understand, you're used Vpp by mistake and actually you're talking about Vpk which is a half of Vpp. Isn't it?

But there is also unclear if you're talking about loaded output or HiZ.

Usually Chinese sig gen show you HiZ voltage. It means voltage for the case, when you don't load sig gen output with a load.

If you connect something to sig gen, include oscilloscope or voltmeter, the actual voltage will be different. Because voltage will depends on the load impedance. For example oscilloscope 1:10 probe usually has 10 MOhms impedance. And oscilloscope 1:1 probe usually has 1 MOhm impedance.

Since sig gen has 50 Ohm impedance and your load has R impedance, it turns into voltage divider

U = U_HiZ * R / (50 + R)

If you load sig gen with 50 Ohm it turns into:

U = U_HiZ * 50 / (50 + 50) = U_HiZ / 2

When I view the output of the sig gen with the approx 50 ohm resistor across the signal and ground pins, the scope will only see a sine wave of about 1.50Vpp at the transformer "input" (secondary coil). So that in theory I should get 15.95Vpp approximately at the output (primary coil), which is closer to the 16.2Vpp which the scope shows in real.

this is incorrect measurement. Remove any 50 Ohm resistor across the signal and use high impedance probe (at least 1:10) to measure amplitude on the transformer input.

Why does the signal from the sig gen have such a significant difference from the expected 2Vpp output, when terminated with the approx 50 Ohms?

You're needs to look at transformer as impedance transformation device.

Also you're needs to take into account source and load impedance. This is very important!
Because result will depends on both - source and load impedance and impedance transformation ratio of the transformer.

Transformer impedance ratio is a square of turns/voltage ratio.
Since you're mentioned turns/voltage ratio is 10.6345, then:

impedance_ratio = 10.6345 ^ 2 = 113

But actual impedance ratio will depends on the transformer properties which depends on the coils coupling, core properties and frequency.

Let's assume that impedance_ratio at 1 kHz is 113 and signal generator output is 50 Ohm, then you're needs to load transformer with:

Zload = Zsrc * impedance_ratio = 50 * 113 = 5650 Ohm

In such case you will get max efficiency and output voltage will be about 10.6345 higher than input.

If you put transformer output to a different load, then transformer input impedance will be different.
It will leads to sig gen impedance mismatch and as result, worse efficiency and different voltages on the input and output coils.

[maelh]

When putting 5650 Ohm (roughly with a potentiometer) at the output of the transformer, the scope measures 19.6 to 19.8 Vpp at the output of the transformer for 20kHz, gradually going down to 16Vpp when reaching 1kHz. At the higher end of the frequencies, it looks rather good.

The variation also makes somewhat sense, since when setting the LCR to measure at 1 kHz the primary is 618.5mH and secondary is 5.469mH (same as in the initial post),
but when the LCR is set to 10kHz, it measures 1176 mH at the primary and 172 µH at the secondary. Quite a significant variation in inductance.

Then again I am surprised that it looks closer to 20Vpp at 20kHz or 10kHz on the scope (as opposed to the 16Vpp at 1 kHz) when the LCR meter does measure values that would assume another turn ratio, TR = 82.69 at 10 kHz.

[maelh]

As I understand, you're used Vpp by mistake and actually you're talking about Vpk which is a half of Vpp. Isn't it?
But there is also unclear if you're talking about loaded output or HiZ.

I think it is really Vpp, since this is the name of the automatic measurement of the scope, and when verifying "by hand" (looking at the scope's gradicule), the positive and negative peak of the sine wave have the voltage difference given by Vpp. The scope is probing with high impedance setting (10x probe).

The siggen specifies a 2Vpp for a 50 ohm load (50 Ohm load setting was used throughout this topic), when setting to Hi-Z it will half the displayed value (on the sig gen, the output remains unchanged).

[radiolistener]

The variation also makes somewhat sense, since when setting the LCR to measure at 1 kHz the primary is 618.5mH and secondary is 5.469mH (same as in the initial post),
but when the LCR is set to 10kHz, it measures 1176 mH at the primary and 172 µH at the secondary. Quite a significant variation in inductance.

Then again I am surprised that it looks closer to 20Vpp at 20kHz or 10kHz on the scope (as opposed to the 16Vpp at 1 kHz) when the LCR meter does measure values that would assume another turn ratio, TR = 82.69 at 10 kHz.

That is normal. Any transformer has a limited working frequency range.
Outside that frequency range it's parameters will be out of specification.

Don't expect that transformer will works the same for very wide frequency range.

[radiolistener]

I think it is really Vpp, since this is the name of the automatic measurement of the scope, and when verifying "by hand" (looking at the scope's gradicule), the positive and negative peak of the sine wave have the voltage difference given by Vpp. The scope is probing with high impedance setting (10x probe).

Then your sig gen show you Vpp for HiZ, it means that it shows voltage for open output connector (when nothing is connected to the output connector). Since it's output is 50 Ohm, you're needs to calculate real amplitude on the sig gen output with connected load:

U = U_HiZ * R / (50 + R)

where R is your load impedance. For example if you use 10x probe with 10 MOhm impedance, then R=10000000.

Note, that transformer input impedance depends on the load connected to the transformer output.

When putting 5650 Ohm (roughly with a potentiometer) at the output of the transformer, the scope measures 19.6 to 19.8 Vpp at the output of the transformer for 20kHz, gradually going down to 16Vpp when reaching 1kHz. At the higher end of the frequencies, it looks rather good.

you're needs to take into account that your potentiometer may have some inductance, also there is some resistance of transformer coils, which also should be taken into account.

If your potentiometer inductance is not high enough to affect your measurement at 1-20 kHz, then it means that there is different impedance ratio for 1 kHz and 20 kHz in your transformer. This is normal behavior, for example if you're trying to use low frequency with trasformer which is designed for a high frequency. Very low frequency requires higher coil inductance.

[maelh]

Then your sig gen show you Vpp for HiZ, it means that it shows voltage for open output connector (when nothing is connected to the output connector). Since it's output is 50 Ohm, you're needs to calculate real amplitude on the sig gen output with connected load:

I think I didn't explain myself well. If I connect a 50 ohm BNC cable, with a 50 ohm bnc termination to the scope, and set the sig gen to 2 Vpp assuming a 50 Ohm load, it will ouput pretty close to 2Vpp on the scope as well. So, direct sig gen to scope connection, with just a bnc cable and a bnc termination.

If I switch the sig gen to Hi-Z and use no 50 ohm bnc terminator, then it also shows the value I set on the sig gen.

So that part seems fine (when no transformer is involved).

[maelh]

That is normal. Any transformer has a limited working frequency range.
Outside that frequency range it's parameters will be out of specification.

Don't expect that transformer will works the same for very wide frequency range.

Yes but why do I have close to 20Vpp for 10kHz (eventhough the LCR measured inductances a 10 kHz suggest a TR of about 83 or about 7000 induction ratio, instead of 10)?

Is the measurement of the LCR wrong, and should I only use the one at 1kHz?

[radiolistener]

Yes but why do I have close to 20Vpp for 10kHz (eventhough the LCR measured inductances a 10 kHz suggest a TR of about 83 or about 7000 induction ratio)?

it may be because coil inductance is not enough for 1 kHz. Low frequency requires high coil inductance. This is why transformer for a low frequency requires more wire turns. But as a side effect, more wire turns leads to a high parasitic capacitance between winding and it is bad at high frequency, so the low frequency transformer will works bad on high frequency.

As I said before, transformer parameter may change significantly on different frequencies, because there is different properties of transformer core, parasitic capacitance, coil inductance, etc. So, you're needs to perform all measurements on the same fixed frequency. For other frequency transformer parameters may be different.

Another possible issue is that your variable potentiometer may have different impedance at 1 kHz and 10 kHz. Try to put about 5k metal film resistor and compare result with the same resistance on your variable potentiometer. Is there any difference?

What kind of transformer you're using. Is it RF transformer or low frequency transformer?

[maelh]

It's a small transformer (1 to 2cm^2) from an electronics kit, and unfortunately without much additional information. But it is intended for connecting to a speaker. I contacted the manufacturer, let's see if they have a datasheet.

[Zero999]

The variation also makes somewhat sense, since when setting the LCR to measure at 1 kHz the primary is 618.5mH and secondary is 5.469mH (same as in the initial post),
but when the LCR is set to 10kHz, it measures 1176 mH at the primary and 172 µH at the secondary. Quite a significant variation in inductance.

Then again I am surprised that it looks closer to 20Vpp at 20kHz or 10kHz on the scope (as opposed to the 16Vpp at 1 kHz) when the LCR meter does measure values that would assume another turn ratio, TR = 82.69 at 10 kHz.

That is normal. Any transformer has a limited working frequency range.
Outside that frequency range it's parameters will be out of specification.

Don't expect that transformer will works the same for very wide frequency range.

The original poster might now be thinking "It should be fine at 1kHz, because it's an audio transformer."

To answer that. The audio transformer will be probably be designed for driving an 8 Ohm speaker on the secondary, the coil with the fewer turns. The voltage is too high at 1kHz for the transformer to work properly. Reversing the transformer, so it steps down the voltage will fix that. It's often possible to run a transformer at higher voltages than it's designed for, by proportionally increasing the frequency, as long as the insulation will take it of course.

To be pedantic: transformers don't amplify. If the voltage is increased, the current is proportionally reduced. An amplifier boosts both the voltage and current, but requires an external power supply, as perpetual motion isn't possible.

[radiolistener]

To be pedantic: transformers don't amplify.

yes, it transforms impedance.
But I think it's okay to say about voltage gain of transformer (if output impedance is higher than input).

[CaptDon]

Why are you trying to be so scientific about your measurements?? Transformers are weird creatures, the primary will have some
self resonant frequency, the secondary will have some different resonant frequency and the transformer as a whole will have an even different self resonant frequency. Any measurements made at or near those frequencies could be abnormally higher or even lower depending on your drive circuit and if the resonance was series or parallel. You will find that the transformer will present different load impedances at different frequencies and just because your signal generator has a 50 ohm output impedance and you properly terminated it at 50 ohms so that when you set it for 2vpp or .707rms that is the voltage it will produce AT 50 OHMS!!!! If you look at the actual voltage being applied to your transformer it will vary with frequency. Try turning the frequency down to 10hz and see that the transformer practically swamps the sig gen to almost no output. You have spent so much time and effort using science to prove or disprove a turns ratio and have only proven to yourself these methods CAN ONLY APPROXIMATE!!! Accept the fact. You may as well try to prove which is bigger 6 or half a dozen.

[SilverSolder]

[...]
Are such larger variances normal? If so how would you use a transformer "reliably"?

This all depends on the quality of the transformer.

The magnetic circuit in a transformer is not ideal.  The magnetic core material is not ideal, and the shape is not ideal either, causing leakage of magnetism through the air, outside the core. 

The non-ideal behaviour is strongly frequency dependent.


Transformers can be made close to ideal, but now they become big and expensive.  A high quality signal transformer can go from below 1Hz all the way up to nearly 50KHz,  ruler flat.

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