...The radios we'll always remember


 Posted By: Robert Nickels (W9RAN)
Posted: 02/21/2023

Tech Library 0 Comments 02/21/2023 

What is Q?

and how to measure it using the ringdown method


What is Q? 

A concise definition:   "In physics and engineering, the quality factor or Q factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is."

We know it's important in RF circuits - low Q coils or tuned circuits will result in loss and perform inefficiently.   We may remember from the Handbook that the Q of a coil equals the ratio of X/R,  that is inductance divided by resistance.    Thus to make high Q coils we use larger diameter wire to reduce the resistance, and wind the coil on low-loss materials and do other things to maximize the Q.    

But how do we know what the Q of a tuned circuit actually is?     Everything that vibrates or oscillates has a resonant frequency, and as the above definition implies, a high Q factor means the signal is more undamped than a low Q factor circuit.

A good analogy is to think of a tuning fork or a bell, which once struck continues to vibrate for a long time.   But if we touch it with our fingers, we "dampen" the vibrations and the ringing stops.     If we were to drape a cloth over it, the resonant frequency could still be heard, but very faintly and it would die out instantly, because of the increased damping.  In fact Q is just the recipricol of the damping factor, and refers to the same measurement.

If you go by the Q value displayed on a handheld meter or RLC type bridge, you can be assured it is lying to you.  That's because these meters only measure at one or a few low frequencies, such as 100kHz max.    They can't tell you what the Q factor of an RF circuit actually is at the frequency it is to be used.

Fortunately there is a very simple solution to this dilemma.   The following test setup will allow measuring Q by the ringdown method:

No Image Found


Ringdown works exactly like the tuning fork example.   Instead of whacking the fork with a hammer, we use a square wave generator to hit it with a square wave - but the effect is the same.   The fast-rising edge of the square wave, connected to a small inductive loop, excites the tuned circuit with a magnetically-coupled pulse and in response, the tuned circuit "vibrates" at its resonant frequeny just like striking the tuning fork does.   To see this response we need an oscilloscope and to make it easy the trigger input from the scope is obtained from the square wave generator.     The frequency of the square wave is a small fraction of the RF frequency of the LC circuit - a few kHz will do just fine.    Suitable square wave and function generators are available at reasonable cost and the only other thing required is a 10X scope probe to prevent the oscilloscope from loading the circuit excessively.

Every time a new square wave starts the output voltage rises rapidly which causes a corresponding induced voltage to flow in the circuit under test.     After this "hammer strike" the stimulus is quiet for a comparative long time - long enough for the response to completely die out.     I used a 1 kHz square wave so there was an impulse exciting the tuned circuit under test ever 1 ms and by setting the  trigger controls on the scope a waveform like this was captured:

No Image Found

For this test I set the function generator for a 1 khz square wave, at 15 volts.   The output was connected to a two turn loop that would positioned near the circuit under test to obtain a good display.   The scope is set for 100 ns per division or as desired to get a full screen display.   The cursors have been set to the highest peak and 1/2 this value, but eyeball is good enough since Q is not a precise measurement.   The time difference between peak and 1/2 peak is just the number of cycles and we can easily count them (=2 cycles).   The Q of this circuit is thus 2 * 4.53 = 9.   If more cycles are present (i.e. higher Q) than can be counted easily, the process is just to measure the number of division betwee the peak points and multiply by the time per division.

So what does this tell us about Q?       Well, there is a mathmetical relationship that can be boiled down to the amount of time required for the signal response to drop to 50% of it's peak value.     Skipping the mathmetical derivation, it comes to:

Q = Pi * N(number of cycles) /  ln(2)  - - which can be solve to  Q = 4.53*N

(seel the link below if you don't believe me!)

So all we need to do is determine the number of cycles it take to where the signal has dropped by 1/2, and multiply by 4.53 to get Q.    The derivation of that number and a more detailed descripton of the ringdown method and some examples can be viewed HERE

Anyone wishing to use this method is highly encouraged to read the information at the link above.   If you want to learn how to make really good high Q tuned circuits, this is the easiest way to do it and to KNOW that your measurement reflects how the circuit will actually work at the intended RF frequency.    One of the examples shown is a magnetic loop antenna, where any reduction in Q is going to translate directly into how good and usable the antenna is going to be.

Additional references can be found at the link as well


   

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