Measuring the Q  of  LC circuits.

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In theory we can determine the Q of a circuit as follows:

Step 1
Couple a RF signal generator to the LC circuit.
The coupling between generator and LC circuit must be loose, otherwise the output resistance of the generator will load the circuit and reduces the Q.

Step 2:
Set the generator to the frequency at which you want to measure the Q.
Adjust the LC circuit (turn the tuner capacitor) so you have maximum voltage over the circuit, the circuit is now in resonance, this frequency is the resonance frequency of the circuit (f.res).

Step 3
Measure the voltage over the LC circuit at resonance frequency (f.res).

Step 4:
Vary the generator frequency a little above and below f.res. and determine the two frequenties were the voltage over the circuit is 0.707 times the value at f.res.
The voltage reduction to 0.707 times, is the -3 dB point.
One -3 dB point, is lower in frequency then f.res, this frequency we call: fl.
The other -3 dB point is higher in frequency then f.res, this frequency we call: fh.

Step 5
Calculate the bandwidth BW:   BW= fh - fl.
Calculate the Q:     Q= f.res / BW

For performing these 5 steps, we can use the following test setup's:

Test setup 1  Measuring the Q with a signal generator and a probe. In the schematic above you see from left to right the following components.
A signal generator
A coupling coil
The LC circuit
A 1:100 oscilloscope probe
An oscilloscope

Connect the output of the signal generator to the coupling coil having e.g. 50 turns.
Place the coupling coil at about 20 cm from the coil of the LC circuit.
The coupling coil don't have to be high Q.
Because of the 20 cm distance, there is a loose coupling between the coils.

Connect the probe to the LC circuit.
The earth connection of the probe must be connected to the housing of the tuner capacitor.
The probe is connected to the oscilloscope.
The probe provides a small loading of the circuit, so the Q will not reduce so much.
There are also 1:1 and 1:10 probe's, but these will load the LC circuit too much.
The 1:100 probe I use has a input resistance of 100 M.Ohm, and a input capacity of 4 pF.

The output voltage of the generator must be set so high, that the oscilloscoop gives a clear picture of the RF signal.
Because the 100 times attenuation in the probe, the signal generator output must be set fairly high.
When measuring low Q circuits, I must set the generator output to it's maximum of 20 Volt peak-peak.

For measuring the Q: perform the 5 steps described on the top of this page.

The frequency adjustment is done by hand, by turning the frequency knob of the generator.

Test setup 2   Measuring the Q with a sweep generator and a probe. In this schematic you see from left to right the following components:

A sweep signal generator
A coupling coil
The LC circuit
An 1:100 oscilloscope probe
An oscilloscope

This method uses a sweep generator, this is a signal generator where the frequency is constant varying between two set values.
I use a sweep function generator of brand "Hung Chang" with model number G305, it can produce signals up to 10 MHz.
It has a "sweep output" which gives a voltage going up and down with the frequency sweep.

The "sweep output" is connected with the X input of the oscilloscope, the oscilloscope is placed in the X-Y mode.
Now the lightspot on the scope runs from left to right and back over the screen, this makes a frequency scale with on the leftside the startfrequency and on the rightside the stopfrequency of the sweep generator.
The sweepfrequency must be set at about 10 Hertz, this means the frequency is running 10 times per second from startfrequency to stopfrequency and back.

The Y input of the oscilloscope is connected via the 1:100 probe with the LC circuit.

The RF output of the sweep generator is connected to the coupling coil, which is placed  about 20 cm from the coil of the LC circuit. At the top: the sweep signal generator. Under: oscilloscope with the curve of the LC circuit on the screen.

We can turn the tuner capacitor and get the curve of the LC circuit on the oscilloscope screen.
Adjust with the amplitudeknob of the sweep generator the hight of the peak of the curve to 2.83 cm.
(The peak-peak distance is then: 2x2.83=5.66 cm).

Determine the width of the curve at 2 cm high, this is the -3 dB point (because 2.83x0.707= 2).

Calculate the bandwidth:
BW= (stopfrequency-startfrequency) x curve width at -3 dB / total screenwidth.

And the Q:
Q= f.res / BW

The great advantage of this method is that changes in resonance frequency of the LC circuit, can direct be seen on the screen.
Also changes in Q can direct be seen, because the hight of the peak will change then.
At high Q circuits, we can see the hight of the peak halve for instance, when we touch the (insulated) litzwire with our fingers.

Test setup 3     measuring the Q with a sweep generator and a amplifier. In this schematic we see from left to right the following components:

A sweep signal generator
A coupling coil
The LC circuit
An amplifier
An oscilloscope

When using a 1:100 probe between LC circuit and oscilloscope there are two problems:

a- Because the 100 times attenuation of the signal, the amplitude on the oscilloscope will often have a very low level.
b- The probe can give dielectric losses, which reduces the Q.

To solve these two problems, I replaced the probe by a selfmade amplifier with a gain of 1x.
The amplitude on the oscilloscope will now be 100 times higher then with the 1:100 probe.
The input of the amplifier uses a FET (Field Effect Transistor) and a capacitive voltage divider, which will load the circuit only very little.

A complete schematic of the amplifier you will find here

For the rest, this test setup is the same as test setup 2.

test setup 4   Measuring the Q with a DDS signal generator and a amplifier. In this schematic you see from left to right:

A DDS signal generator
A coupling coil
The LC circuit
An amplifier
An oscilloscope

DDS means "Direct Digital Synthesis".

The output signal is in a DDS generator made in a digital way.
The great advantage of this kind of generator is the accuracy of the frequency setting.
The output has also a very low distortion.
The DDS generator I use, is a build yourself electronic kit from the company  ELV .
You can also buy a complete build and tested module.

The specification are:

Output frequency: 0.1Hz -- 20 MHz.
Output voltage: 0 -- 4 Volt peak peak (not loaded).
Output impedance: 50 Ohm.
Minimum stepsize of frequency setting is 0.1 Hz. (up to 10 MHz output frequency).
Minimum stepsize of frequency setting is 1 Hz. (10 to 20 MHz output frequency).

As stepsize you can also select, e.g. 10 Hz, 100 Hz, 1 KHz, etc.  Circuit board of the DDS generator. DDS Generator build in a box.

I now use the DDS generator because the used sweep generator could not be set accurate enough on frequency.
And also the frequency changes slightly during the measurement. Photo of the test setup.
The coil laying on the table is the coupling coil.
The FET amplifier is connected via short wires to the tuner capacitor.
The coil of the LC circuit is placed at the top of a wooden stick, so it has not much influence from surrounding obstacles.

The windings are laying in a horizontal plane, so the coil picks up less signal from radiostations which can influence the measurement.

During measurements on high Q circuits, I tune the DDS generator in 10 Hz steps.
This test setup is in my opinion very reliable for determining the circuit Q.

Tips for measuring the Q:

During measurements don't come with your hands too close to the LC circuit, because this has influence on frequency and Q.
Keep a minimum distance of 20 cm.

Don't lay the coil of the LC circuit during measurement on the table, but keep a minimum distance of 20 cm from wooden or metal objects.

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