Tapering to a reasonable degree is preferable to avoid sharp nodes for a VSWR mismatch. Now, if you taper for too long, then you just have a large amount of line that is a sub-optimal impedance. It really is a matter of what you're shooting for in terms of insertion loss/VSWR/space tradeoffs. I always consult the microwaves101 website for nice rules of thumb but I usually go 5-10% of a wavelength if I have the room. It looks like you have a good two step taper there but you haven't provided any sizing so I can't be sure.
Sometimes, the circuit might want a capacitive stub on either side of an inductive length such as this.
Note: My experience tends to be in the 26 GHz and below range so please take my advice with a grain of salt.
The modes of a waveguide refer to the distribution of the electrical and magnetic fields across the cross-section of the waveguide.
The electric field going to (roughly) zero at high-conductivity surfaces (like the inner and outer conductor of a coaxial line) places boundary conditions on the differential equations describing the waveguide behavior. This leads to patterns in the way the fields distribute themselves across the waveguide area. If a certain E/M field pattern can propagate along the waveguide without changing, we call that a mode of the waveguide.
Generally there will be only one propagating mode at low frequencies, and additional modes will be able to propagate as the signal frequency increases.
The waveguide modes are important because different modes tend to propagate at different rates along the z-axis of the waveguide. Generally you want to operate a waveguide at a frequency where only a single mode is supported. At higher frequencies, a single pulse input into the guide might exit the other end highly distorted due to the different propagation velocities of the different modes.
Different mode structures can also create reflections at the connection between two transmission lines, even if both transmission lines have the same characteristic impedance.
I have also heard about single and multimode fibers in optical communication. Are they the same?
Yes, it's essentially the same. Of course, the frequencies at play are very different. And the boundary conditions are created by changes in dielectric constant of the material rather than conductive surfaces.
Best Answer
A rule of thumb cannot really be true or false. It does not belong to science, but to to engineering or practice. So it can be useful or not useful. The basic idea, at an intuitive level is that a short waveguide will not effect the signal much, because the reflection gets back to the source before the source phase has changed much (recall that for a sine wave, phase advances linearly at a constant rate with time). The big problems caused by reflections have to do with creating minima and maxima in space on the waveguide and self cancellation associated with that.
In digitial circuits, it is similar, but it is the rise and fall time that matter, not the frequency. If the rise/fall time is long compared to the waveguide flight time, then impedance matching is not needed. Because the reflection will get back to the driving source while the edge is still changing. So in other words, the source feels the load, even though there is a mismatch at the transmission line.
Another way to look at it is this. (This is highly non-technical.) When a source puts energy into a waveguide, it does not know what the load looks like. It only knows what the waveguide looks like. It does not receive any feedback from the load until energy reaches the load, reflects, and comes back to the source. If the waveguide is long, and the mismatch is large, then the feedback, when it arrives, may be far out of phase with the source. This can cause big problems. But if the waveguide is short, the feedback will not be far out of phase, and all will be well, even if the mismatch is larger. And if the load is perfectly matched to the waveguide, then there will be no reflection, no feedback, and all will be well.
One last thing. This has to do with RF propagation in the presence of obstacles. In order for an RF wave in space to be reflected (or absorbed, for that matter), you need an object of a certain size with respect to the wavelength. Longer wavelengths tend to refract around small objects. This happens with waveguides also. If the waveguide is "small" the energy sort of refracts around it.