In most countries, you need to pass an examination to get an amateur radio license. In the US, the question pool is public, so a big part of studying for the license consists of going through the whole question pool and making sure you know the answers to every question. One of them tripped me for a bit:

T8A11
What is the approximate maximum bandwidth required to transmit a CW signal?
A. 2.4 kHz
B. 150 Hz
C. 1000 Hz
D. 15 kHz


(To normal people, a CW signal is a “beeping Morse code signal”.)

Now, a CW signal is pretty much a sinusoidal wave, and I knew that a pure sinusoidal wave takes a tiny, tiny bandwidth, so I could eliminate answers “A”, “C”, and “D” straight away. That left “B”, but I didn’t know why it would be the right answer, so I had to think about it for a while.

It is true that a sinusoidal signal takes very little bandwidth. If a CW signal consisted just of a steady sinusoidal carrier that never turned off and on, it would indeed have an extremely low bandwidth, only limited by the transmitting oscillator’s stability.

However, a CW signal is not a steady sinusoidal; it is modulated. In particular, it is modulated by turning it off and on according to a message that’s encoded using Morse code. This modulation causes the CW signal to have a bigger bandwidth than a steady carrier.

As an extreme, we can imagine that we want to transmit a series of Morse dots at 30 words per minute. That would be equivalent to switching the carrier on and off 25 times every second. That’s a 12.5-Hz signal that, when modulated, requires a 25-Hz bandwidth at the very minimum (12.5 Hz on each sideband). In practice, the required bandwidth would be higher, depending on how abruptly the carrier was switched on and off.

To demonstrate it, I wrote a widget to simulate a CW signal being received by a CW radio with a filter centered at 600 Hz. It can play the received signal on your speakers and show its frequency spectrum on your screen. The top half displays an instantaneous chart (with horizontal lines every 40 dB), while the bottom displays a waterfall plot. The vertical lines indicate the frequency of the received signal, with dashed lines every 500 Hz and continuous lines every 1000 Hz.

Let’s first look at (and listen to) a transmitter that produces a signal with very abrupt off/on and on/off transitions. Go ahead and press “Play”:

As you can see, when the carrier is steady on, the signal does not use much bandwidth; it is when the signal switches on or off that it uses a lot of bandwidth. This bandwidth usage depends on how sudden the on/off transitions are. Above, the switches were instantaneous, so the signal uses a lot of bandwidth, which is not good.

To avoid using so much bandwidth, many radio transmitters ramp the signal up and down over 5 milliseconds instead of cutting it on and off. This lowers the bandwidth usage without really affecting the sound. You can check it out by pressing “Play” on the widget below:

That’s not the whole story, however. The widgets above simulate a radio with a receive filter, so they don’t show the whole bandwidth that’s used by the signals. The widgets below had their filters removed, so they can show how much bandwidth is really used in each case. The one on the left is the original signal that switches on and off suddenly, while the one on the right is the modified signal with 5-millisecond transitions:

The difference is undeniable. On the left, the on/off transitions appear as broadband energy spikes that are almost as powerful as the signal itself across the whole band. On the right, the spikes still produce quite a bit of power, but it occupies a smaller bandwidth and their power goes down faster as they get further from the central frequency.

The huge amount of power produced by sudden on/off switches causes an annoying effect, called “key clicks”. Press “Play” on the widget below to hear it:

In this widget, there is a signal being transmitted 2800 Hz above where we are listening, so it’s outside of what the filter will let through and we can’t hear it. However, the filter lets through some of the energy that comes from the carrier being switched on and off, and it can be heard as clicks.

These “key clicks” are very annoying since they could even drown out real signals and they can often be heard quite far away from the signal’s frequency, so if your transmitter produces clicks, other amateur radio operators will be quick to find you to tell you what they think of your radio transmitter.

On a transmitter with a 5-millisecond ramp time there isn’t so much power outside of the signal, so the filter doesn’t let so much energy through and there are no clicks. Press “Play” on the widget below to hear the result:

This is the part where you can do your own experiments with key clicks. Here are two widgets you can try: the left one is clicky, while the right one is not clicky. Both have a slider you can use to modify the signal’s frequency and see where the clicks are present, or where the signal is louder than the clicks.

Found anything interesting? Let me know what you think!