# Measuring air transformer at resonant frequency

• voidnoise
In summary, the conversation discusses the development of an air transformer and the challenges encountered in measuring current, mutual inductance, and efficiency. The setup includes two identical inductors and a series LCR circuit. The confusion arises from a mismatch in impedance and the use of voltage instead of power measurements. The conversation also mentions the optimal load on the secondary side and methods for calculating it. A recommended circuit with five nodes is also provided for measuring mutual inductance.
voidnoise
Hi,

I am in the process of trying to develop an air transformer but encountering unusual behaviour which I hope can be explained with some fundamental theory I don't yet know. My set up is as follows;

- Two identical wound 13.3uH inductors designed to resonate at 4.364MHz. They are 10 turns, 2mm pitch, 100mm diameter, 1mm core. Each coil is designed to be part of a series LCR circuit where the capacitance is 100pF, and the resistance is 100ohm.

- The primary coil is powered by a 20Vpp signal generator, 50 ohm output, using a co-ax cable with measured capacitance between the lines of 90pF.

- I am not sure of the full effect of the transmission line capacitance which would be parallel to the LCR circuit, but to compensate I have used a variable capacitor (instead of the designed 100pF) to tune the primary back into 4.364MHz.

- The secondary side is a closed LCR, 13.3uH, 100pF and 100ohm.

- I am using two separate oscilloscopes so that no grounds etc. are shared to confused measurements.

The confusion: I am trying to measure current through each of the 100ohm resistors to infer the mutual inductance, co-efficient of coupling and efficiency. This is done by measuring the voltage across the resistor and then using ohms law. Measurements show that at close range less voltage and so less current passes through the resistor in the primary circuit than the resistor in the secondary circuit. This would hint at more power out than being put in would it not?

It might be easier to talk in terms of watts. P=IV.

Compare the two wattages. Does the secondary use more wattage thru the 100 ohm resistor?
And if you are comparing wattages, don't you need to compare the wattage of the entire loop...L, C, and R? Actually, you would have VA with the L and C...but since at resonance, perhaps it would be just Watts across the resistor...?

What does "close range less voltage" mean in your last paragraph?

1 person
I think you may have a few misconceptions about transmission lines and networks in general. If you have a 50 ohms resistive load fed with a 50 ohm transmission line, then it makes NO DIFFERENCE how long the line is (neglecting loss). The length only makes a difference when there is a mismatch.
-
You have set yourself right off the bat for a mismatch when trying to drive 100 ohms with a 50 ohm source.

Thanks psparky. I have been playing around with the circuit a bit more and getting a better understanding about the equipment. Power is definitely the correct way to go. I think my original confusion is due to my ignorance of transmissions circuits, but I am a bit better read up on now. Averagesupernova I am sure you are correct about need match the load to the source impedance, but how would you deal with circuits that have varying impedance with a change in frequency?

One thing I have noticed is that there is an optimal load on the secondary side, would anybody know a way to calculate what that would be? I would assume that it can be inferred from the calculated/estimated emf? Which would also mean that it would vary with distance between the two coils.

voidnoise, are the components on the each side connected in series or parallel? What is the purpose of the 100 ohm resistor? When you speak of load on the secondary, are you referring to the 100 Ω resistor or an additional load? In what sense do you mean optimum load, maximum power dissipation or some other criteria?

The easiest way to measure the mutual inductance is to excite one coil with a known current / frequency and measure the voltage induced in the second.

Using the following equipment, build a circuit with five nodes:
1 - Ground and input of an oscilloscope.
2 - Ground and output of a 200kHz sine wave generator.
3 - a low inductance 10 ohm resistor, R12 (i.e. 1/4w is good)

The Nodes are associated as follow:
node 0 - (ground) scope ground (chan 1), signal generator ground, R1 (pin 1)
node 1 - (signal source) signal generator source, primary (pin 1)
node 2 - (current measurement) primary (pin 2), R1 (pin 2), scope input (chan 1)

node 3 - scope ground (chan 2), secondary (pin 1)
node 4 - scope input (chan 2), secondary (pin 2)

Adjust the signal generator as high as practical at 200 kHz and measure the current using R1 (V chan 1 / R1)
In this condition, measure the voltage of the coupled sine wave on the secondary (chan 2).

L = V(Chan2) * R1 / [ V(chan1) * 2 * pi * f ]

voidnoise said:
Thanks psparky. I have been playing around with the circuit a bit more and getting a better understanding about the equipment. Power is definitely the correct way to go. I think my original confusion is due to my ignorance of transmissions circuits, but I am a bit better read up on now. Averagesupernova I am sure you are correct about need match the load to the source impedance, but how would you deal with circuits that have varying impedance with a change in frequency?

One thing I have noticed is that there is an optimal load on the secondary side, would anybody know a way to calculate what that would be? I would assume that it can be inferred from the calculated/estimated emf? Which would also mean that it would vary with distance between the two coils.

Are you sure you are measuring Power and not just VI? The phase can make a lot of difference.

Sophie,
You're correct, there is an optimum load which is inclusive of shunt capacitor on the secondary coil to tune out its leakage inductance. When working with implants, the EEs built a huge variety of coils and tested them over various orientations.
I found you can approximate the same work (within 10%) using MathCad and treating the leads as filaments. Once you have the self inductance and mutual inductance of the coils, just pop it into LTSpice to get a feel of how the system behaves.

- Mike

## 1. How do you measure air transformer at resonant frequency?

In order to measure an air transformer at resonant frequency, you will need a network analyzer or a vector network analyzer. Connect the input of the analyzer to the primary winding of the transformer and the output to the secondary winding. Set the analyzer to measure the magnitude and phase of the signal, and then sweep the frequency range until you find the resonant frequency where the magnitude is at its peak and the phase is at 0 degrees.

## 2. Why is it important to measure an air transformer at resonant frequency?

Measuring an air transformer at resonant frequency allows you to determine the transformer's resonant frequency, which is the frequency at which the transformer will have the highest efficiency and the least amount of losses. This information is crucial for designing and optimizing transformer circuits, as well as for troubleshooting and diagnosing any issues with the transformer.

## 3. What factors can affect the resonant frequency of an air transformer?

The resonant frequency of an air transformer can be affected by various factors such as the size and geometry of the transformer, the material and thickness of the windings, the distance between the windings, and the dielectric properties of the surrounding medium. Other factors like temperature and humidity can also have an impact on the resonant frequency.

## 4. Can you measure an air transformer at any frequency?

No, an air transformer should be measured at its resonant frequency in order to accurately determine its efficiency and other important parameters. However, you can also perform measurements at different frequencies to characterize the behavior of the transformer and understand its performance under different operating conditions.

## 5. How does the resonant frequency of an air transformer affect its performance?

The resonant frequency of an air transformer is directly related to its efficiency and losses. At the resonant frequency, the transformer will have the lowest losses and the highest efficiency, resulting in better overall performance. If the transformer is not operated at its resonant frequency, it may experience higher losses and reduced efficiency, leading to potential issues with the circuit or system it is a part of.

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