OK, it's established that harmonics work like picking up a 100kc crystal calibrator in a ham receiver every 100kc's up the band. But do harmonics work in reverse? Like if you needed to calibrate the 60kc IF in a Hammarlund HQ 170 and your signal generator only goes down to 100KC's, can you put it at 120 and get your needed 60? And for that matter, how about third or 4th harmonics to do the multiplex decoder of a stereo FM tuner?

No....

Harmonics are higher frequencies that result from some kind of distortion of the waveform of the "fundamental" frequency (note). If a lower-frequency signal is present, then it becomes the fundamental.

Here's a way to visualize it: if you have distortion in an amplifier, it does the same thing on every cycle of the waveform being processed. Thus the basic repetition cycle is still at the frequency of the fundamental.

For extra credit, consider what happens when two frequencies are present. If there is no distortion, you get out just what you put in. But, with the right kind of distortion, the frequencies will mix...producing new ones at the sum and difference frequencies.

It get's worse, but I'll take a break for now.....

There is something called subharmonics, but I have little knowledge of them.
Apparently, they are of a much lower magnitude than harmonics when they appear, and only certain electronic circuits are prone to producing them.

Harmonics are integral multiples of the original frequency. The first harmonic is the fundamental (original) frequency. The second harmonic is 2X the fundamental. The third harmonic is 3X. Simple enough but sometimes people think the first harmonic is twice the fundamental; it isn't.

Another distinction to be made is the difference between harmonics and overtones. Electronic equipment produces harmonics, not overtones. But mechanical things, including quartz crystals, generally produce overtones. Overtones are approximately, but not exactly 2X, 3X, etc. the fundamental frequency. Overtones result from such second order parameters like the diameter of a piano string while the fundamental is controlled by it;s length.

Crystal oscillators can produce outputs at higher frequencies than the fundamental frequency of the crystal. These frequencies can be either harmonics or overtones depending on the circuit. If the circuit is arranged so that the crystal oscillates at it's fundamental frequency and the multiplication happens separately, the result is harmonics. However, if the circuit forces the crystal to vibrate in one of it's higher modes, then the result is an overtone since the physical second order properties of the crystal are now in control.

You can't get a lower frequency than the fundamental out of an oscillator without using a frequency divider or by mixing the output of two oscillators together.

Subharmonics are easy with ex-sand electronics. Especially
any power of two, or the 1-2-5-10 sequence.

The downcount to align a 50 kHz IF works fine .. even from
10 MHz. Of course they generate square or rectangular waves.

I posted a 1MHz or 100 kHZ calibrator circuit using them with
a cheap 2 MHz crystal. Works great and vastly cheaper than 1 MHZ
or 100 kHz crystals. Switchable 100 kHZ or 1 MHz.

However, there is a well-known method to down-convert using
an analog circuit and tubes. See the Racal RA17 circuit. Its a royal
pain to adjust.

Big difference between harmonics (caused by some form of non-linear behavior of a device or component), and the aribitrary frequencies available by using dividers.

See other posts in re divider circuits (which use active components)...

One thought: distortion produces harmonics, but cannot produce sub-harmonics. Distortion is a passive process, whereas divider are active.
Can we show that getting a lower frequency requires an active device?

Corollary: can anyone demonstrate how you would get sub harmonics with a passive device?

One common application of the word "subharmonic" refers to high frequency transmitters that use frequency multipliers to reach the final output frequency. If the transmitter has inadequate shielding and filtering, it is possible for the output of the oscillator or one or more of the multipliers to escape and be radiated. These would be "subharmonics" of the desired frequency but are actually harmonics of the oscillator. This is especially likely to occur when the final amplifier is also a multiplier. Then the "subharmonic" is present in substantial amplitude and there is the least filtering before the antenna.

A circuit called a 'blocking oscillator' will produce sub harmonics.
Look at the old RCA tube type color bar generators. They have many
and are a royal PITA to fix. Of course these are active circuits.
Steve

If we are talking about the same thing, a blocking oscillator is simply a circuit that goes into saturation or cutoff during part of its cycle. How would that make subharmonics?

To make subharmonics, you have to have something that causes and event or action that occurs every other cycle of the fundamental. How would a blocking oscillator do that?

By setting it's natural frequency of the blocking oscillator somewhat lower than the desired "subharmonic" and using the input frequency to synchronize it. it can be done but an IC counter is easier to make work.

Got it!-- I had a bit of "Neuron slowdown" there......still takes an active circuit to make subharmonics, n'est-ce pas?

An edge triggered 'T' flip flop will divide by 2. Counters are made from
these.

One way to visualize how a blocking oscillator works is think
of it as an amplifier tuned to a subharmonic of its input and
right on the edge of oscillation. I've only run across these
at freqs below 1 MC.

Don't know of a way to produce subharmonics without
an active device.
Steve

I recall a "Sub-Cycle" box which generated 20 Hz ringer voltage from 60 Hz - it had only inductors, capacitor and a transformer. I did a search and found a manual: https://www.telephonecollectors.info/in ... erter/file (I suspect there is a non-linear element - maybe the inductor. There is a relay required to start - operates once at power-on).

Frequency division can occur with non-linear circuits, which we may not consider active - with neon bulbs, saturable inductors, diodes. A mechanical analog - a loose shoelace flopping right / left - half the step rate.

A passive non-linear circuit will be determinisitic with repect to the input signal. IOW, each allowable value at the input has a unique corresponding value at the output. Such a circuit cannot do frequency division. To do so requires that something different happens each time the input is at the same value.

if you have a passive resonant circuit, you can get a few cycles of oscillation when you apply (any) signal. A subharmonic oscillation cannot be sustained however because the input signal does not contain that frequency component.

What remains is---eg---an active resonant circuit tuned to an integer fraction of the input signal. Can this be synced to the input?

I think the 20 Hz ring generator uses a choke that is saturating on every third cycle (or two of 3 cycles)of 60 Hz, so that there is a 20 Hz component to drive the resonant circuit. The starting relay give a pulse that pushes it into saturation - it wouldn't reach that level with just applied 60 Hz. Once it's started, it's 60 Hz in, 20 Hz out.

Diodes have capacitance that varies with voltage (if we USE that feature, we usually call them varicaps or VVCs). So we can make a resonant circuit with an inductor and diode, that DOES respond differently on every other cycle of applied RF, dividing by two - I think some passive RFID tags use this circuit.

My spider sense tells me that some laws of physics are being threatened.......Can we see some example circuits?

The manual posted above has the circuit for the 60 Hz - 20 Hz ring generator (for phone ringing voltage).

1985 Patent for the RFID application https://patents.google.com/patent/US4670740

My brain hurts..... I think the secret is that the 20Hz tank is drawing power from the AC source---but how? If I weren't fully booked, I'd be in the lab building something. (Trying to remember where I put those 20Hz transformers...... )