Part 13 
by Dick Kelly, W6BKY, w6bky@aol.com

First, a couple of corrections to Figure 2 in last week’s column: R5 should be 33k; it was erroneously shown as 3.3k. Also, the .05 uF capacitor that was labeled C17 should have been labeled C16.

Figure 1, below, shows the 10.58 to 10.74 MHz VFO oscillator circuit. Yes, this is the same circuit that was presented last time, but I’ve re-drawn it to show the Colpitts oscillator more clearly. "L" is approximately 1.5 uH; 19 turns in a T50-6 core (yellow). The value of C6 is found experimentally. I used 69 pF (a 47 pF and a 22 pF in parallel). More about this during check-out. 

"L" and the V V C along with C6 make up the parallel-tuned circuit that determines the frequency of the VFO. The V V C is an MV2104. Capacitors marked with an asterisk must be silvered mica, COG, or NPO.

You might wonder how the component values for the resonant circuit are determined. Well, when Jupiter is aligned with Mars, and Mercury is on the cusp of a new moon, if the inductive reactance equals the capacitive reactance, then we have a resonant circuit. For any given frequency there are endless combinations of L and C that will produce a resonant circuit. Experience shows that variable capacitors and V V C’s in the 5 pF to 300 pF range are altogether practical. Combine this with the fact that a 1.5 uH coil and a 150 pF capacitor resonate near the frequency of interest, and you have the component values for this VFO’s resonant circuit. You can find formulas for figuring all this out in your Handbook, if you like to do arithmetic. The component values actually used in the circuit take into account "stray" inductance and capacitance that occurs in the real world. More about this during check-out.

RESONANT CIRCUITS are fascinating critters! While I’m NOT going to get into a theoretical discussion, there are some fundamental characteristics of resonant circuits that you (and I) should keep in mind when building VFO’s, filters, RF amplifiers, etc.

Two types of resonant circuits are commonly used: series resonant circuits and parallel resonant circuits, as shown below. Here are two important things to keep in mind: PARALLEL resonant circuits attenuate the flow of AC current at the resonant frequency (and pass all other frequencies); SERIES resonant circuits pass AC current at the resonant frequency (and attenuate all other frequencies).

Figure 2

One practical application of a resonant circuit is the RF choke. When talking about a choke, "choke" is a noun. When talking about what a choke DOES, however, "choke" is a verb. (Ahhh, the grammar of electronics!) My dictionary defines choke: "… to stifle or smother …". That’s exactly what we want an RF choke to do; smother RF current at a particular frequency or group of frequencies. A favorite term used in electronic prose is "de-couple". Whatever term is used, RF chokes stop (or, at least diminish) RF current. So, what kind of a resonant circuit is an RF choke?

A parallel resonant circuit, of course!

Just to make things interesting, any given choke will act differently at different frequencies. (For DC, a choke acts like a piece of wire.) At some frequencies, it will act like a resistor (a parallel resonant circuit) and at other frequencies it will act like a series resonant circuit. Some RF "chokes" don’t choke at all. These are sometimes called "peaking coils". 

If you look closely at a choke, you see only coils of wire. (There are ferrite "chokes" that are not wire at all, but that’s another story.) Alert readers, such as yourself, may be wondering where the capacitive reactance required to form the resonant circuit in an RF choke comes from. Well, there is capacity between the windings on a choke, and this capacity is what yields resonance in a choke. Now, here’s a question for you: How does one measure the capacity between windings of a coil?

Give up? I thought so, because it can’t be done (not directly, anyway). The capacity can only be inferred from the resonant frequency of the choke. OK, so how do you measure the resonant frequency? There are several ways to do this, the easiest of which is to use a grid dip meter, or Grid Dip Oscillator, (GDO) as they are called these days. 

Speaking of the GDO, if you plan to do much tinkering with RF circuits in the HF spectrum, get one! Other than the VOM and oscilloscope, the GDO is the most used instrument on my work bench. I don’t think anyone manufacturers new GDOs these days, but you can find used ones at Hamfests and flea markets for fifty bucks, or so. I suggest you get a solid state GDO (as opposed to a tube-type) because they are more versatile.

Once the resonant frequency is known, the capacity can be calculated, assuming, of course, that you know (or can find) the inductance of the coil. Inductance can be measured using any number of clever devices. 

Another important consideration when working with resonant circuits is that of the inductance to capacitance ratio (L/C ratio). Other things being equal, best selectivity (narrow bandwidth) is obtained in a series resonant circuit when the L/C ratio is high. As you recall, there are endless combinations of inductance and capacitance that will yield resonance at any given frequency. If you want good selectivity in a series resonant circuit, the L/C ratio must be high. An example: either of the following L/C combinations will yield resonance at about 7.1 MHz … 25 uH and 20 pF or 1 uH and 500 pF. The first combination (25 uH and 20 pF) will give the better selectivity. If, on the other hand, broad bandwidth is desired, the second combination should be used. (Neither of the above combinations is practical in the real world; I’m using them to illustrate a point.)

For parallel resonant circuits, things are just the opposite. I won’t go through an example for parallel resonance - you get the idea, I’m sure. Once again: if you want to REALLY understand this stuff, arithmetic is required, and I’ll let you plow through the formulas in your ARRL Handbook, if you feel compelled to do arithmetic.

Speaking of formulas, even they can be simplified. For resonant frequency, try:

This formula, it seems to me, is much simpler and easy to work with than those you usually find in the ARRL Handbook, and elsewhere.

Another formula you might find handy for calculating the values for coils and capacitors in resonant circuits is:

With this formula, if you know the value of either L or C, you can readily find the other. For example, suppose you want a resonant circuit for 7.1 MHz, and you have an 8 uH coil on hand. What value of capacitor do you need? You know (from the formula) that 

You also know that L=8 uH, so …

Is this the way I find values for capacitors and inductors in resonant circuits? Nope. I use my handy-dandy "L/C/F CALCULATOR, Type A" slide rule that was marketed by the ARRL for several years. This simple slide rule has saved me countless hours (days?) of tedious arithmetic. Too bad the ARRL no longer sells the device. 

All this arithmetic has given me a headache, so I think I’ll take a nap. Next time, we’ll take a close look at VFO tuning, VFO buffers, and I’ll show a parts layout for the VFO.

'Til next time, 73, Dick, W6BKY