Sound test

Signals and waveforms

What is a signal?

Need not be electrical

Morse

Speech

Video

Contains information

Signals have shapes – waveforms

Water waves – height Audio – sound pressure

Audio – electrical voltage

Electrical waveforms are variations in voltage

AC mains has a waveform but is not a signal.

BITX20 bidirectional SSB transceiver

BITX20 bidirectional SSB transceiver

LO BFO

Mic

Mixer

MixerIF FilterRF Filter

Antenna

Transmit direction shown

Summary of our radio waveforms

Audio Frequency (AF)

Beat Frequency Oscillator (BFO)

Intermediate Frequency stage (IF)

Local Oscillator (LO)

Radio Frequency stage (RF).

Lets look at the waveforms

We start with the input Audio Frequency

Many of the waveforms are sine waves

Later we will look at why

Why Sine waves are important

They are natural

They are as fundamental as the circle

All other waveforms can be broken down into sine waves (More on this later)

A graph of a Sine Wave

Time ->

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Another natural Sine Wave generator

1 2 3 4 5 6

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Plotting waveforms

ScaleAxesOriginTime axis AmplitudeFrequencyNegative axesScope time base

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The sound of waveforms

The note A above Middle C is defined to be 440 HzHere is a pure sine wave at 440Hz

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Time in seconds->

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Other waveforms

Here is a Square wave at 440Hz (A above Middle C)

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Time in seconds->

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Fundamentals and Harmonics

In general fundamental frequencies are sine waves.

Any waveform can be broken down into a fundamental sine wave and its harmonics.

Harmonics are 2,3,4 etc (i.e. integer) times the fundamental frequency.

A square wave can be shown to consist of a fundamental (of the same frequency) plus only odd harmonics.

The harmonic content of a square wave

A square wave has a 3rd harmonic of amplitude 1/3 plus a fifth of amplitude 1/5 etc.

If it is a perfect square wave these go on forever.

(Being a symmetrical waveform it has no even harmonics)

We will add the harmonics one at a time and inspect them.

3rd Harmonic

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Playing just the harmonic

Time in seconds->

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3rd Harmonic added

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5th Harmonic also added

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7th Harmonic also added

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Fundamental and odd harmonics up to 15

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There are a total of 7 notes playing

Compare our original square wave

A Square wave at 440Hz (A above Middle C)

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And compare our original pure sine wave

Here is our pure sine wave at 440Hz again

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Linear and non linear systems

We have seen that waveforms can be broken down and rebuilt by adding sine waves.

This only works well for linear systems (i.e. if you can trust addition.)

For example if in your system doubling the input signal doesn’t double the output signal you have a non-linear system.

Non linear systems

In a linear system when you apply a sine wave of frequency F you just get a sine wave of frequency F out.

In a nonlinear system you also get some harmonics at frequencies 2F, 3F etc. (only odd ones if its symmetrical)

E.g. if you seriously overdrive an amplifier with a sine wave you will get something like a square wave.

Non linear systems

In a linear system when you apply two sine waves of frequency F and G you just get frequencies F and G

In a nonlinear system you also get sine waves at frequencies F+G and F-G.

(You also get all the harmonics and all the sums and differences of the harmonics)

The ideal mixer

Another day we will look at the electronics of mixers.

An ideal mixer multiplies rather than adds waveforms.

If you feed two sine waves at frequencies F and G into a multiplier you just get sine waves at frequencies F+G and F-G and no harmonics.

Rather than prove this using maths this lets look and listen.

The inputs to the ideal mixer

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2000Hz

2200Hz

The output from the ideal mixer

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200Hz

4200Hz

and

Comparison sounds to check the output

200Hz

4200Hz

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Some maths

Did you notice the output waveforms were 90 degree phase shifted sine waves of half the amplitude?

For many purposes this makes no difference

Sin(f)* Sin(g) = Cos(f-g)/2 – Cos(f+g)/2

My last graphs allow for the phase shift. A mathematician would call them cosines but they are still sine waves.

BITX20 bidirectional SSB transceiver

LO BFO

Mic

Mixer

MixerIF FilterRF Filter

Antenna

Transmit direction shown

Questions?