# Capacitor Q investigation

## How Do We Test The Q Of a Capacitor? Or, why are varactor diodes so awful in a VCO?#

I asked this question to myself Sunday night (1/9/19). By the morning I was still keen to get an answer. In the end, this exploration didn't lead me to any clarification on how to extract the Q. factor for a particular capacitor. Instead, it did lead to a demonstration of an important difference between varactor and air spaced variable capacitors.

I interrupted my good friend Hans Summers very busy workflow to ask, "How Do We Test The Q Of a Capacitor?"

He was really busy, so he said,  "Don't know. No idea. Google research required."


However, to me, the Q of a capacitor seemed mashed-up by google and results included "Q measured in Coulombs, V in volts and C in Farads!"

"This is Q but not the Q we want. LOL (its physics O level)," I said.


### ⚛ I Did Find A Nice Yet Not Helpful Waffle-Description#

In physics and engineering, the quality factor or Q factor is a dimensionless parameter that describes how under-damped an oscillator or resonator is, and characterises a resonator's bandwidth relative to its centre frequency. Note: This refers to a scalar quantity or a quantity of dimension one

Hans did one search on google and got better results than me in hours! His first hit was a page with the following information:

The Q factor of a capacitor, also known as the quality factor, or simply Q, represents the efficiency of a given capacitor in terms of energy losses. It is defined within the following formulae:

Qc ={Xc \over Rc} = {1 \over ω0C Rc}

Where QC is the quality factor, XC is the reactance of the capacitor, C the capacitance of the capacitor, RC is the equivalent series resistance (ESR) of the capacitor, and ω0 is the frequency in radians at which the measurement is taken.

In an AC system, the Q factor represents the ratio of energy stored in the capacitor to the energy dissipated as thermal losses in the equivalent series resistance. For example, a capacitor that is capable of storing 2000 joules of energy while wasting only 1 joule has a Q factor of 2000. Since Q is the measure of efficiency, an ideal capacitor would have an infinite value of Q meaning that no energy is lost at all in the process of storing energy. This is derived from the fact that the ESR of an ideal capacitor equals zero.

The Q factor is not a constant value. It changes significantly with frequency for two reasons. The first reason is the completely obvious ω0 term in the above equation. The second reason is that ESR is not a constant value with regard to frequency. The ESR varies with frequency due to the skin effect, as well as other effects related to the dielectric characteristics. (this is for relatively normal capacitors and not for a varactor, where the situation gets even more complex)

A related term, called the dissipation factor(DF), is sometimes established in capacitor data sheets instead of the Q-factor. In AC circuits the DF is simply the reciprocal value of Q.

## ⚛ Easy right? Yes It Ain't Half Bad At All...#

It is nice to have a definition, so the key points of the above blurb are:

1. The Q factor of a capacitor, also known as the quality factor, or simply Q, represents the efficiency of a given capacitor, and this efficiency is inversely proportional to the capacitor's energy losses.
2. The Q factor is not a constant value.
3. The first reason for the above lack of constancy, is the totally obvious ω0 term in the above equation.
4. The second reason is that ESR is not a constant value.
5. The ESR varies with frequency due to the skin effect, as well as other effects related to the dielectric characteristics.

Note: If the key points above make no sense to you at all, then it might be that this article is at the wrong level of discourse at this time. 1

## ⚛ So How To Measure The Q Of A Capacitor?#

So, what are the practical steps needed to measure the Q or Quality of a capacitor?

### ⚛ Qualitative method#

When we try to measure this illusive mysterious Quality or Q factor, we rapidly choose qualitative methods, as we do not have the required CERN or NPL budget to buy expensive test laboratories, staff the same and tread-on meaningfully, with long beards, around the sacred particle accelerator3...

You may discover which qualitative methodological modes of investigation are preferred for this type of problem when on a low budget, by reading-onward. In other words this is probably not Maincore. However, it is supremely interesting!

### ⚛ Build A Colpitts Oscillator#

Crocodile clips are now banned!

This web-page shows crocodile clips! These are now Banned under the new acts of international preservation of radio kits rules. The author4 of this page did twice blow up and totally destroy two excellent QCX kits provided by Hans Summers. After the first catastrophic crocodile clip occurrence, the work bench of the author (who had claimed that he had removed all such clips), did secretly keep a few too many crocodile clips on board. These things are -f nasty: they have a habit of slipping; they can cut through quality solder resist layers on a nice Chinese PCB; when working with a through-hole double layer PCB, the crocodile clip may decide to touch the underside of the board while it is powered up under test. This effectively shorts the current from point A to point B. If you are lucky, this may do nothing, if not then, as the author discovered, you will find that almost every chip on board is completely bricked and subsequently many hours spent patiently replacing everything may result in nothing more than total frustration.

### IN SEARCH (SETI)#

So, while still in search of the mysterious 'quality factor', we build a colpitts oscillator using a ceramic resonator. This is done so we can pull the frequency of the ceramic resonator with capacitance from a varactor diode or other variable capacitor. Subsequently and importantly, we (still not royal) shall be able to measure and take a look at the output from the oscillator and study what differences, if any, are to be found when using different types of variable capacitor to 'pull' the frequency away from the centre frequency of the resonator.

Note

Partial orthogonality may be present here. Basically from the formulae above we see that the Q factor is essentially increased when the Resistance quotient of the lumped impedance is decreased. Ergo: The use of and comparison between varactor and air spaced capacitors in this context contains other areas of enquiry that have little to do with resistance. This includes, yet is not limited to, the capacitance effect produced by a reversed-biased diode being a product of not only the DC element of the circuit, but also the AC component. As such, we do expect the varactor diode to suffer perturbations in capacitance and this phenomena is apparent with each rise and fall in current.

### ⚛ The Schematic Of This Easy Circuit#

M0OOZ - YooFab / CC BY NC ND

Note: This colpitts circuit has a number of features that are important in this context.

1. There is a Potentiometer under the emitter before the 1K resistor to ground and this pot may be used to improve the quality of the output by stopping the oscillator transistor from clipping.

2. The oscillator is buffered with an emitter follower, such that we don't load down the oscillator in any appreciable manner when measuring with an oscilloscope or other test equipment.

3. There is no inductor placed in the AC path, often used to extend the range of pulling.

4. This is not a free running oscillator, it is a ceramic resonator controlled colpitts oscillator. This is not as rigid as a crystal controlled oscillator. However, we make use of this lack of rigidity by 'pulling' the ceramic resonator much further than is possible with a crystal.

5. The design of the oscillator is robust and lends itself to experimentation as well as being great for use in Radio applications.

### ⚛ Ugly#

M0OOZ - YooFab / CC BY NC ND

1. The colpitts is built ugly style so we can get the -f on with it, and so that we can change things easily.
2. Just to strengthen this point, this style of prototyping is rapid! You design your schematic and then lay the board out as closely to the schematic diagram as possible. Very often you do not need jumper wires at all, which is not the case with VEROBOARD, which also suffers from inductance and capacitance effects due to the close proximity of the copper strips.
3. There are notable persons who slag this style off saying "feebis methods" or worse.
4. While the end result is undoubtedly not polished, it is highly suitable for prototyping and can be used to make finished items (with a little more care).
5. It is also built upon ground plane, which even at HF is important.

### ⚛ Nasty Signal#

M0OOZ - YooFab / CC BY NC ND

So, we are interested in the way a varactor diode, or other variable capacitor might affect the Quality of the wave shape.

### ⚛ Surgically Removed 1n4007 Diode#

M0OOZ - YooFab / CC BY NC ND

After surgically removing the 1n4007 diode, we (non royal) move on to newer and greener pastures. Specifically, we take a break from thinking and we make the leads needed to connect an air-spaced variable capacitor.

### ⚛ Air-Spaced Variable Capacitor#

M0OOZ - YooFab / CC BY NC ND

1. The nice air spaced capacitor is ready to use in our (liberal use of collective unconsciousness terminologies) oscillator.

2. No other tampering changing or fiddling with the circuit is undertaken.

3. The oscillator is fired up ready for taking butchers (look) at the output wave signal for comparison with that of the signal produced when the diode was used.

### ⚛ Bigger Pull, And Generally A Better Signal#

M0OOZ - YooFab / CC BY NC ND

Excuse the -f out of focus photo here, but note the 7129 kHz frequency and the niceness of the wave.

### ⚛ The Other End Of The Pull Range#

So, now we take a good butchers at the other end of the pull range from this resonator based colpitts oscillator.

M0OOZ - YooFab / CC BY NC ND

So, this is a better photo shot of the scope showing a frequency of 7017 kHz and a good-looking signal that stays looking great across the range.

## ⚛ Conclusions#

1. The purity of the wave is different with the diode than when an air spaced variable capacitor is employed.

2. It is nasty looking with the diode, whereas with the air spaced C it is great.

3. The diode causes horribleness and distortion.

4. The air spaced capacitor does not cause this horror.

5. The pulling range of the diode and variable capacitor vary by 10 kHz in this setup.

1. The variable capacitor has a range of 113 kHz.

2. The diode has a range of 90 KHz.

### ⚛ Why?#

1. OK so why does the diode do this?
2. Why does the diode make an uglification of the job?
3. Why do people use diodes if this is what they do?
4. Why don't we use variable capacitors any more?

#### ⚛ Not Very Probable Answers#

1. 😉The diode resonates to the subtle but powerful effects of Celebrity Cult Leaders.

2. 😉Manufacturers know that we use cheap 1n4007 diodes as varactors; they alter these cheap ones to make them awful, so we have to buy expensive ones instead.

3. 😉Extraterrestrial lifeforms or/ and politicians are interfering with our minds.

4. 😉We don't use air spaced variable capacitors because foreign powers have taken control of all manufacturing facilities and are stock piling the capacitors as a prime survivalist measure.

## ⚛ Watch This Space#

None of the above are true, yet if you tune in soon to this space, more information on this phenomenon may appear.

## Footnotes:#

1. The apparent lack of fluidity with comprehension is a big problem and it is natural that at first sight, a pressing desire is to throw Aristotle into a burning bush. You might choose other lifestyles that are less stressful; you could jump up and down in muddy puddles; you could read-on until you have properly assimilated all the words, in the hope that at least some of this gibberish will make sense; you might return to this page at another time?

2. A list of components is often referred to as the BOM (Bill Of Materials)

3. Staff at CERN and other places have been reported to ponder upon the meaning of it all, whilst pacing slowly along the sacred particle accelerator. They do this for years; beards grow long while the thatch atop such folk thins out until the thatch-event-horizon occurs.

4. The Author here is Geoffrey David Cowne (M0OOZ)