In particular, this would be a fairly low frequency VCO with a frequency range of 10 Hz to 20 kHz. I'm thinking of the configuration with the T-junction that has 2 opposite facing, reversed biased varicap diodes and a resistor perpendicular to the intersection point.
Can Zener or Schottky diodes be used as a substitute for varicap diodes in tuning a VCO?
Yes they can, depending on the circumstances.
A varicap diode is similar to a "normal" silicon diode, however the diode is designed such that the junction capacitance under reverse biased conditions is more predictable, has a more linear relation to the reverse voltage and sometimes also has a larger value.
A Zener diode is similar to a "normal" silicon diode, however the reverse breakdown voltage has a more predictable value. Besides that, it also has a reverse biased junction capacitance just like any other diode.
A Schottky diode also has a reverse biased junction capacitance which is also dependent on the reverse voltage.
So all three diodes (normal, Zener, Schottky) have "varicap" behavior so can in principle be used.
However, the varicap is better optimized for the task, see my paragraph about the varicap above.
Also, the Zener and Schottky diodes have some disadvantages which may render then useless in some applications.
They often have a higher leakage current. Especially the Schottky diodes have high leakage at high temperatures.
They might be more noisy. Especially the Zener diodes are known to be noisy (inject noise into your circuit).
They might have a capacitance with a lower quality factor. This is due to the series resistance of the diode's capacitance. Such a series resistance might lower the Quality factor of your tuning circuit or oscillator tank. This might lead to lack of loopgain in your oscillator so the oscillator will stop oscillating. The series resistance might also inject additional noise.
So yes, possible but there are some "gotchas" you have to be aware of.
It is impossible to design a VCO with a frequency range of 0 Hz to 20 kHz using a DC controlled Varicap bridge due to the limitations of C1/C2 at V1/V2 is limited to <<100:1 best case and more often much less. e.g. 30:1V might achieve 60:1 C ratio in a half bridge voltage-biased diode-capacitance regardless of size being 1mA or 1kA diode.
Consider this. How many decades down is DC from 20kHz??
3 dec.(20Hz) or more? Thus 2 decades is even exceeding this requirement.
This why Spectrum Analyzer designs Up-convert the signal or use the VCO above the fmax to sweep then tune the VCO over a max of 50% range, then mix to down-convert at some IF to span a wide range of many decades.
Thus, another approach is needed, which exists. Any questions?
I just whipped up this DC to 20kHz (>6 decade) VCO triangle square output only. Effectively the 0 to 0.1Hz is only mV levels on the fine VCO input with coarse on 0V. Using Rail to Rail +/-10V OPA with any small signal logic level NMOS FET.
Each trace has different time scales to demonstrate 0 to 20kHz. You can change the 5V bias parts to simplify using +/-10V or single supply.