ARLA/CLUSTER: Episódio 206 da série "Foundations of Amateur Radio"

[João Costa > CT1FBF]

Foundations of Amateur Radio #206

SDR: How many colours inside a Software Defined Radio?

If you were asked to make an image of the Sydney harbour bridge and
only use four dots, the viewer might struggle to determine what was
the bridge, the sky, the water and the Sydney Opera House. Regardless
of the number of colours available to you, the number of dots would
not be enough information for most people. You might have a nice piece
of art on your hands, but it might be ineligible for the Archibald
prize. Even if you were allowed many colours, and just four dots,
figuring out if the blue dot was water, sky, or the background of the
Australian flag on top of the bridge might be just as complicated.

If you were asked to make the image with one hundred dots, and only
use black and white, from the perspective of the viewer you'd have a
result that was easier to understand. Use a thousand dots, even
easier, even if you only used black and white.

Now, if you were to use a hundred dots, with ten colours, your image
might be just as easy to understand as if it was a thousand dots in
black and white.

The point is, there are two things going on here. The number of dots
and the information contained in each dot.

More dots or more colours, or both, will help your image.

Similarly, in Software Defined Radio, more dots, that is, more
samples, will help and as I've previously mentioned, you need at least
twice the number of samples as the highest frequency that you're
measuring. But what of the colours in relation to an SDR?

Measuring voltage as a human with a piece of paper is pretty
straightforward. Provided you've got a Volt meter, a piece of paper
and a scribble stick, you're good to go. If you measure your voltage
as 1 Volt, you write 1, if it's -1 Volt, you write -1. Similarly, if
it's 100 Volts, you'd write 100, 13.8 Volts and you'd write 13.8.
We'll get back to colours in a moment.

Provided your paper is big enough, you can record as many values as
you need and as accurately as you desire. 13.8 or 13.8853, makes no
difference to a piece of paper.

Computers represent numbers internally using powers of two, called
bits. A single bit can represent two values, 0 and 1. Two bits can
represent four values, 8 bits represent 256 values and 16 bits
represent 65536 different values.

The takeaway is that there are a specific number of values that you
can represent inside a computer, depending on how many bits you use.

Consider the values I've mentioned, 1, -1, 100 and 13.8. That's four
different values. If it's not immediately obvious, what ever solution
you come up with, tracking positive and negative, tracking small and
large, whole and fractions should all be part of the mix. In case
you're wondering, we're essentially describing here how many colours
or values we are going to allow, or in terms of a computer, how many
bits.

Let's consider all the values you might measure and represent inside a
computer. How many different voltages do you want to be able to record
between 1 Volt and 100 Volt?

If you allow for ten values, you can record 10 Volt, 20 Volt and
so-on, but you can't record 15 Volt.

If you allow for a hundred values, you can record 1 Volt, 2 Volt and
up, but you won't be able to record 1.5 Volt.

If you account for a thousand values then you can record 1.1 Volt, 1.2
Volt and so-on, but you can't record -10 Volt.

Remember, our computer representation can only manage a specific list
of values and the size of the list is determined by the number of bits
you're using.

The rabbit hole goes even deeper.

Radio signals vary massively in their strength, which is why we use a
decibel scale to represent the signal strength, instead of saying
station A is a thousand times stronger than station B, we say it has a
signal level that's 30 dBm higher. That's comparing a 1 Watt station
to a 1 kilowatt station, and in terms of voltage, that's between 20
Volt and 632 Volt.

If you're designing a mechanism to store your measurements inside a
computer, you might decide to use dBm to record your measurement.
Let's say 30 values from 30 to 60 dBm. Sounds great, where do I sign
up?

Not so fast. What happens if our station is running less than 1 Watt,
or if it's running 100 kilowatt, like when you happen to receive a
nearby FM broadcast station?

Not only do you need to contend with a whole range, called a Dynamic
Range of measurements, you also need to deal with what happens to the
overall picture.

Let me say that in another way.

Your voltage measurements at the base of your antenna are a
representation of the RF information that your antenna is receiving,
or transmitting for that matter. Representing that inside a computer
means that the values you're using, and how fast your gathering them,
determine how well the RF signal is represented.

One thing to note is that the largest values represented by what ever
you choose is only part of the problem.

A signal that is stronger than the largest value you can record is not
going to be recorded correctly. Similarly, a signal that is so small
that it doesn't register as a change, also has an incorrect recording.

Picking the right combination of dots and colours, sample size and
bit-depth, doesn't end there, because there's even more to this, but
I'll leave that for next time.

To blow your mind, the Dynamic Range, bit-depth and sample size I've
talked about in relation to Software Defined Radio, also applies to
many other things, like taking a photo with your digital camera, or
sampling digital audio, so understanding this in one area will likely
help you in other places as well.

he final takeaway is that a computer records a range of values that
can represent a measurement in the real world. Picking the correct
range of values determines how well your computer represents what your
measuring


I'm Onno VK6FLAB