In article , Paul Burridge
writes:

What's the maximum multiplication factor it's practical and sensible
to attempt to achieve in one single stage of multiplication? (Say from
a 7Mhz square wave source with 5nS rise/fall times.)

Paul, past state of the hardware art (past 60 years) indicates that
triplers are the practical maximum. Quintuplers have been done
but those are rare in described applications.

In 1955 I had hands-on experience with a septupler (7 x multiplier)
using a 2C39 and a cavity-tuned plate circuit at 1.8 GHz. That was
in a General Electric microwave radio relay terminal designed about
1950. Of nine terminals, two had to "QSY" to new crystal-controlled
microwave center frequencies for second-level contingency operation.
Difficult and fussy to do but was do-able...the crystal was also 7th
overtone in a vacuum tube oscillator but was followed by a buffer
stage feeding a tripler, another buffer, then the septupler which fed
another 2C39 as the pulse-modulated final for 12 W peak output at
1.8 GHz. [from memory and 35mm slides...big GE manual went to
recycle a long time ago] That's the only septupler application that
I am aware of...no doubt there are others, somewhere.

General Electric must have had some division/work-group with lots
of work in old frequency control methods. A local NTSC color sub-
carrier generator-regenerator made by GE had extensive use of
"locked oscillators" for frequency multiplication and division, but
mostly at frequencies lower than 7 MHz. Haven't come across any
practical hardware on locked oscillators except for two mentions in
older journals, trade papers. One of those used transistors as
active devices.

Doublers and quadruplers have been made using both diodes and
tube-or-transistor active devices. That's relatively easy with non-
square waveforms (distorted sinewaves); square waves have high
odd harmonic energy, low even harmonic energy.

Making practical, reproducible active multipliers in the home shop
is, practically, a trial-and-error process involving playing with cut-
off bias of the active device input, energy and harmonic content of
the source, and Q of the multiplier's output stage. In the past I've
made tripling-in-the-plate pentode crystal oscillators using
fundamental frequency quartz but those were highly dependent on
getting the highest impedance tuned plate circuit and needed
scope viewing to check output waveforms. Not very reproducible.
There's no "easy" way to do it that will "work every time" despite
the claims of many. :-)

Digital division IS straightforward up to about 1 GHz based on
such technology over the last 3 decades. That's why PLLs came
to prominence in frequency control techniques up to UHF.

Len Anderson
retired (from regular hours) electronic engineer person