If by “taper the waveguide down to a point” you mean replacing the flat shorted end behind the probe/feed with a pyramidal or conical taper that gradually narrows to a closed tip, the effect depends on where the taper is located and how long it is.
For a typical 1420 MHz WR-650 feed:
- A flat metal back wall creates a well-defined reflection.
- The distance from the probe to that back wall is chosen so the reflected wave reinforces the probe coupling.
- This arrangement is easy to model and gives predictable impedance matching.
If you taper the back section to a point:
- The reflection becomes distributed
- Instead of one strong reflection from a flat wall, reflections occur gradually along the taper.
- The electrical “short circuit” is less sharply defined.
- Potentially broader bandwidth
- A gradual taper can reduce standing-wave effects over a wider frequency range.
- This principle is used in some broadband horn and waveguide terminations.
- Probe tuning changes
- The optimum probe position would almost certainly move.
- A probe tuned for a flat back wall would no longer present the same impedance.
- Possibly lower Q
- The cavity behind the probe becomes less resonant.
- This can make the feed less sensitive to dimensional errors but may slightly reduce peak performance at exactly 1420.405 MHz.
- Little gain increase
- The taper would not significantly increase antenna gain.
- Most gain comes from the horn aperture and dish (or antenna) geometry, not from the exact shape of the shorted end.
For a SETI Horn of Plenty feed operating solely at the hydrogen line, a properly positioned flat back wall is usually the better choice because:
- Simpler construction.
- Easier tuning.
- Well-understood impedance behaviour.
- Maximum efficiency at a single frequency.
A tapered back section becomes more attractive if you’re trying to cover a wider range (for example 1.2-1.7 GHz) with good matching.
A useful comparison is that the flat-back design behaves somewhat like a quarter-wave backshort cavity, whereas a pointed taper behaves more like a gradually transformed impedance that spreads reflections over a longer distance.