transformer characteristic impedance

i cannot understand what is the characteristic impedance of a transformer used for, is it just for finding the leakage inductance and magnetizing inductance at different frequencies??

Can you provide some additional information?

WimRFP said:

Can you provide some additional information?

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my Prof. ask me to measure the characteristic impedance of toroid coil at 100KHz, he said i can adjust the turn ratio to match the impedance between the load and the signals generator. but i know the impedance of signals generator is 50 ohm, the turn ratio is easy to test as 1.3:1. so i can connect a load as 50/(1.3^2) to match the impedance. why i need to care about the characteristic impedance at 100KHz. by the way, the transformer is used to measure current signals from 1kHz to 5MHz, he said 100KHz is in the middle of 1KHz TO 10MHz, but i still dont understand how this characteristic impedance can be used to design something or what???

I would ask in a first place: what is transformer characteristic impedance? Obviously it's neither leakage nor magnetizing impedance. I wonder which quantity you gonna measure?

IMHO, the term characteristic impedance can be used for the nominal impedance of connected circuit, in other words it would be defined by the ratio of nominal transformer voltage and current. For some application fields, e.g. audio or RF, (characteristic) impedance specifications are quite common. But it's no property that can be measured directly.

If you can refer to other plausible definition of characteristic impedance, please report.

In certain transformers (transmission line transformers), characteristic impedance of transmission lines is of importance, but for your transformer, I don't see what is ment with characteristic impedance.

Best way (I think), ask your teacher to define characteristic impedance (as applicable to your case).

By carefully trading leakage induction with (winding) capacitance, one can extend the useful frequency range of certain transformers.

yes, you should be test impedance if need, impedace is relation lost question, e.g. you test impedance at difference frequency, if you find the impedance is maximum value at a frequency point, you can say the point is SRF value.

At a lower frequency, toroidal coil is inductor characteristic, however at a higher frequency, toroidal coil is capacitor characteristic, impedance is very complex and sensivity at higher frequency, it is relation temperature and humidity and so on factor.

Below is for reference:

Maybe the question was: "Characteristic OF impedance at 100Khz?

100K is lower frequency, you can test impedance at 100K, impedance is not complex,XL = 2piFL
XC = 1/(2piFC)

zmkm1302022 said:

my Prof. ask me to measure the characteristic impedance of toroid coil at 100KHz, he said i can adjust the turn ratio to match the impedance between the load and the signals generator. but i know the impedance of signals generator is 50 ohm, the turn ratio is easy to test as 1.3:1. so i can connect a load as 50/(1.3^2) to match the impedance. why i need to care about the characteristic impedance at 100KHz. by the way, the transformer is used to measure current signals from 1kHz to 5MHz, he said 100KHz is in the middle of 1KHz TO 10MHz, but i still dont understand how this characteristic impedance can be used to design something or what???

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Apparently you have determined the turns ratio to be 1.3:1, so you could use the transformer to match the 50 ohm generator impedance to a load of 29.59 ohms. But, would the transformer work as well to match 5 ohms to 2.959 ohms; .5 ohms to .2959 ohms; 500 ohms to 295.9 ohms; 5000 ohms to 2959 ohms, etc.? An ideal transformer would be able to match any of those pairs of impedances, but a real transformer would work best at some impedance level. How would you determine the impedance level for best performance? Furthermore, since it isn't a 1:1 transformer, there isn't a single number that would be the characteristic impedance of the transformer as a whole. Each winding, primary and secondary, will have its own "characteristic impedance".

A related question, one answer to which might help you, would be this: given a 10 meter long piece of unknown coaxial cable, what measurements could you make to determine the characteristic impedance (I mean electrical measurements, not mechanical measurements)?

FvM said:

I would ask in a first place: what is transformer characteristic impedance? Obviously it's neither leakage nor magnetizing impedance. I wonder which quantity you gonna measure?

IMHO, the term characteristic impedance can be used for the nominal impedance of connected circuit, in other words it would be defined by the ratio of nominal transformer voltage and current. For some application fields, e.g. audio or RF, (characteristic) impedance specifications are quite common. But it's no property that can be measured directly.

If you can refer to other plausible definition of characteristic impedance, please report.

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i was asked to measure the open-circuit input impedance and short-circuit input impedance of this transformer. then i can find the corresponding leakage impedance Ls and magnetizing impedance Lm at 100KHz, as well as the characteristic impedance Zc=sqrt(ZLs*ZLm). because the frequency response at the turn ratio 1.3:1 with a 50ohm load will be tested. and theoretical result is that the low cutoff frequency at -3dB is at jwLm=Rload (Lm is taught as magnetizing inductance), and the high cut off frequency is at jwLs=Rload (Ls is the leakage inductance). this is a simplified model of this toroid transformer from lecture.

then i can find the corresponding leakage impedance Ls and magnetizing impedance Lm at 100KHz, as well as the characteristic impedance Zc=sqrt(ZLs*ZLm).

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I can try to imagine a reasoning behind the said definition of characteristic impedance, but I'm not aware of it as commonly used technical term. There are stronger candidates, as mentioned by WimRFP and me.

Unfortunately, you have been just asking for the use of the characteristic impedance definition. I fear we can't answer it for the present one.

What value did you get for the characteristic impedance?

Did you consider what I posted: "But, would the transformer work as well to match 5 ohms to 2.959 ohms; .5 ohms to .2959 ohms; 500 ohms to 295.9 ohms; 5000 ohms to 2959 ohms, etc.? An ideal transformer would be able to match any of those pairs of impedances, but a real transformer would work best at some impedance level. How would you determine the impedance level for best performance?"

The Electrician said:

What value did you get for the characteristic impedance?

Did you consider what I posted: "But, would the transformer work as well to match 5 ohms to 2.959 ohms; .5 ohms to .2959 ohms; 500 ohms to 295.9 ohms; 5000 ohms to 2959 ohms, etc.? An ideal transformer would be able to match any of those pairs of impedances, but a real transformer would work best at some impedance level. How would you determine the impedance level for best performance?"

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Hi The Electrician,
do you mean we need the transformer working at a specific frequency when the characteristic impedance at this frequency is at the lowest level?

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FvM said:

I can try to imagine a reasoning behind the said definition of characteristic impedance, but I'm not aware of it as commonly used technical term. There are stronger candidates, as mentioned by WimRFP and me.

Unfortunately, you have been just asking for the use of the characteristic impedance definition. I fear we can't answer it for the present one.

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Hi FvM,
I am not pursuing the definition of characteristic impedance of transformer, but i would like to know how it is used in practice to determine something. for example, can it be used to determine the pass-band of a transformer? this is just my guess. maybe i dont have to concern too much about this characteristic impedance.

I am not pursuing the definition of characteristic impedance of transformer, but i would like to know how it is used in practice to determine something. for example, can it be used to determine the pass-band of a transformer? this is just my guess.

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The value as in your calculation is increasing with frequency. Thus I don't think that the quantity is of much use in a wideband transformer application.

maybe i dont have to concern too much about this characteristic impedance.

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This would be also my suggestion. Measure the well defined Ls and Lm values, they should be fairly frequency independent, and calculate all derived properties, e.g. lower and upper frequency limits of transformer usability based on your source and load impedance.

If you want something with "characteristic impedance" in conventional transformers, sqrt(Ls/Cw) can be of importance.

Ls is the leakage inductance, Cw is the effective winding capacitance for high frequency, measured at same side as used for the Ls measurement.

The ratio says something of the source impedance (or load impedance) that will result in the best high frequency response.

Cw and Ls, maybe together with some external capacitance, may extend the upper frequency range due to some resonance/peaking as appears in CLC low pass filters.

When designing RF transfomers, one has to design the windings in such a way that neither Ls nor Cw dominates. This means that when you are designing a transformer to be driven from 5 Ohms source impedance, you may use wider strip and/or thinner insulation to reduce leakage induction (Ls), as that may dominate in low-Z applications.

On the other hand, when the source impedance is 600 Ohms, one has to use thinner wire and thicker insulation to reduce winding capacitance (as that will dominate in High-Z circuits).

I've never heard the term characteristic impedance in the context of transformers before. Usually it's something similar to what WimRFP stated above, where there is some LC resonance and the characteristic impedance is just the impedance of each component at the resonant frequency. Also applies to transmission lines (though they're not necessarily resonant).

1 KHZ -> 10 MHZ, this is toooo much. I used to work with WB Rf transformers and found it a struggle to meet 50 KHZ to 30 MHZ+- 1 dB. Look out for a ferrite core which is not too low in loss. This will tend dampen out any resonances. The impedance of the windings is paramount, use tightly coupled windings, like 200 mm of wire 1 and 300 mm of wire 2, loosely twist, to get a bifilar (with a bit over). select the wire gauge to be as big as possible to fill the window. You are using sensible terminating resistors, we used 1/2 a turn for 50 ohms, good to < 50KHZ with a Mullard core which had a type number like FX 2249. This was a ferrite block with two holes "drilled" in it through which the wiire was wound. best of luck. By the way "characteristic impedance" is only true for systems that can be cascaded to be self terminating. i.e. if you have a long enough cable, it will look like 50 ohms WITHOUT any termination resistor, likewise filters, stack enough in series and they then look like their characteristic impedance without any resistor.
Frank

Characteristic impedance is a term not often heard in connection with a transformer. If the transformer has windings with different numbers of turns on each winding it would seem that there should be two different "characteristic impedances"; each winding will have its own "characteristic impedance".

However, there is another property known as the "image impedance" that is analogous to characteristic impedance, and is more readily applied to transformers:

https://en.wikipedia.org/wiki/Image_impedance

There is a detailed explanation as it applies to audio transformers:

https://www.electro-tech-online.com...chat/124261-audio-transformers-two-ports.html

If you'll read that thread my further discussion here will tie in with it.

I wound a 1:1 transformer with 20 turns of twisted pair on a ferrite toroid having a permeability of 10000. This toroid is not intended for RF use, but it will serve the purpose of this post.

I measured the open and short circuit impedances of the primary with an impedance analyzer. The first attachment shows those impedances. The vertical scale is logarithmic and has .1 ohms is at the bottom, 10k ohms at the top. The frequency sweep is 1 kHz to 5 MHz. As explained in the referenced thread, the image impedance would be a curve exactly halfway between the two curves shown.

The second image shows the primary impedance as in the first image, but with 3 more curves, showing the effect of loads of 1 ohm, 10 ohms and 50 ohms on the secondary. Notice that the reflected impedance with a 50 ohm load is a nearly horizontal line (it's the second curve from the top) with an impedance of about 51 ohms. This is what we would expect with a 50 ohm load. This reflected load begins to deviate from a constant 51 ohms at the extremes of the frequency range.

The third image shows the impedance (magnitude) and real part of the impedance of the primary with the secondary open circuited. We can see that the impedance comes to be dominated by the losses in the core when the frequency is much above 100 kHz. This is why this core material is only intended for power converter use, not RF use.

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The fourth image shows another sweep of the primary impedance with the secondary open, showing the impedance magnitude and the phase. The phase is the yellow curve, and is shown on linear vertical scale with 100 degrees at the top and -100 degrees at the bottom. The middle of the plot is zero degrees. At low frequencies, the phase is nearly 90 degrees, and the primary impedance looks like a fairly good inductor. Above 100 kHz, the phase begins to tend downward, as the first parallel resonance takes effect. At about 500 kHz, the impedance becomes capacitive. We also know from the third image that the losses have increased greatly.

The fifth image shows the open circuit primary impedance and phase, along with the primary impedance and phase with a 50 ohm resistor connected to the secondary. We can see that the performance at 100 kHz is quite respectable. The mid band of this transformer is fairly centered around 100 kHz. That's where the transformer will work best. I did not design the transformer to be this way; it just worked out and I was surprised.

At 100 kHz, the image impedance of the transformer is around 50 ohms. This shows that knowing the image impedance (characteristic impedance) can help determine the best operating impedance.

Thank you (FvM, Chuckey WimRFPand The Electrician) for your help. Especially The Electrician, i am appreciated for your measurements to explain my concern. I do not have impedance analyzer in school lab. so i only measured the open circuit and short circuit at 100KHz. The following contents are the results on Fri:
I measure the OC and SC impedance at 100KHz, and frequency response from 50Hz to 1MHz.
1. OC and SC test schematic:

OC test, R1 is chosen as 8.4Kohm, and Zoc=3477-j5475 ohm
SC test, R1 is chosen as 51.6 ohm, and Zsc=0.281-j20.41 ohm
the characteristic impedance Zc=334 ohm
i got feedback that Zc is too big, I need to reduce the winding by 0.4 , the current windings are 20 turns : 20 turns.
considering what you said that the transformer impedance should match the generator impedance and load impedance level to get maximum power transfer at any frequency, do you mean that the transformer characteristic impedance is independent of frequency ???

2. Frequency Response of this toroid coil



i found the upper cut-off frequency is at about 250KHz, if I get the transformer's characteristic impedance at a proper level comparing to the source and load impedance, i can also get a wider pass band than the one shown in picture?