Syllabus Sections:- 3M

   SDR transmitters and receivers

Before we dive into this section you should remind yourself of what phases mean as outlined below.

So the concept of phase difference,  is expressed in degrees and that a full cycle is equal to 360 degrees.

Phase

The word phase is used in the context of the waveform to mean an amount of time. The amount of time to do one complete cycle is 360 degree and half a cycle 180 and so on.

As well as measuring time in seconds it is also referred to as so many degrees. Have a look at the diagram below. Note the progression rotates anticlockwise

You can see that there are markings at the bottom of 0 - 180 - 360 which are measurements in degrees. There are 360 degrees in a circle (see diagram above) just as there are in one cycle of the sine wave.

Phase angle

Thus if two sine waves are on the same diagram but start and finish at different places the time difference between them can be expressed conveniently as a phase angle.

Out of phase

NOTE: that the circle on the LEFT denotes rotation ANTICLOCKWISE

The amount that a curve lags or leads is given in degrees according to where the same point on the first curve the second one is. In the diagram above you can see that the angle  = 90^o so by using the circle you could assess the amount of lead or lag in degrees.

From the point of view of the sine wave "A" at point 0, the wave form "C" is leading wave "A" by 90 degrees. If you look at the diagram above "C" as it was at the same point on the time line 90 degree earlier than "A".

Where as wave "B" lags wave "A" by 90 degrees as it has not yet reached the point on the time line where "A" is at 0.

All the waves "A", "B" and "C", above,  are said to be "out of phase".

When trying to assess the amount of out of phase, the leading or lagging of one wave form to another you have to assess the location of the peaks that will indicate to you which wave form is ahead or behind and then consider where they respectively cross the ZERO line as here you will be able to use the graticule to count up the number of degree lag or lead.

In the diagram above the blue wave form is leading the green wave form and the amount of the lead would be assessed on the zero line where the two dotted red line indicate.

In phase

3M1   29   Recall that analogue and digital signals are transmitted by some form of amplitude and/or frequency/phase modulation

In its simplest form a transmitter's RF signal (carrier) is keyed on or off, giving Morse code.
However if the RF signal is modulated by a single tone then you have a real signal in the form of a sine wave.
If the RF signal (carrier) wave form is modulated by audio tones then an AM signal results.
If one side of the AM signal is filtered out (removed) you have USB or LSB with the carrier, but usually the carrier is also filtered out (suppressed).
Similarly with FM (or Phase modulation) it just treats the carrier differently with an audio signal modulated (imposed) upon it.

3M1   29 continued Recall that amplitude and frequency/phase modulation can be portrayed on a phasor diagram.

A phasor diagram is a way to show a rotating vector, also know as a “Phasor” as a line whose length represents both magnitude (“peak amplitude”) and direction (“phase”) which is “frozen” at some point in time.

The phasor diagram in  fig 10.1 p.67  is used to visually represent the single carrier audio tone modulating (or changing) into an RF carrier for USB or LSB, with one sideband rotating in one direction while the other sideband rotates in the other, all at 1 revolution per second. The sum of all three vectors will stay horizontal but can get longer or shorter giving us the AM signal amplitude.

When the carrier is rotated by 90 degrees leaving the original sidebands as they were it gives us narrow band modulation,  the sum of these vectors now moves left to right before rotating again at one cycle per second this movement to the left (anti-clockwise) gives us decreasing frequency and to the right increasing (clockwise). With narrow band the left to right movement is so small as to hardly affect the amplitude,This will give us a second Phasor diagram as shown in fig 10.2 p.67 

3M1   29 continued Understand that to fully capture the information in the amplitude and phases of the signal that the position of the phasors  must be resolved as the values on two axes at right angles.

Please note that the phasors are at right angles but not as you would understand the E (Electrical) and M (Magnetic) waves from an antenna.

If you look at the drawings in on page 68 at Fig 10.3, they each have two axes at right angles. The four axes lines represent the phase, think of the angles between the axes as angles round a circle - so each axis is 90 degrees apart. The dots represent the signal at a moment in time, and the distance of the dots from the centre represents the amplitude.
In drawing A, the two dots are on the same axis, so the two signals are in phase but because they are different distances from the centre, they are of different amplitude.
Drawing B shows two dots which are equidistant from the centre (so the same amplitude) but on opposite axes, so 180 degrees apart in phase.
In Drawing C we see four points the same distance from the centre, so the same amplitude, but each 90 degrees apart from their neighbours.
So - what does this mean in the context of the 3M1 item? Well, we have seen that the drawing lets us express simply both the amplitude and phase relationship of different signals.

3M2  29  Recall that mixing the RF of IF signal with two local oscillators signals 90 degree different in phase will produce an in-phase (I) and quadrature (Q) component which can be digitiesed allowing all forms of modulation to be demodulated entirely by mathematical processes in a PC or using dedicated hardware.

Looking in section titled “SDR Receiver Architecture” Page 68 there is mention of the I and Q terms, and how mixing a signal with two local oscillators 90 degrees out of phase provides an IF which can be converted in two  ADC to give the I and Q outputs.

The most common option to used in SRD  receiver architecture (software design) is to mix two local oscillator signals internally one at 90 degrees different in phase to the other, then the resulting signals can be fed into two ADC or analogue to digital converters which output the I (in-phase) and Q (quadrature) channels for further processing to take place by the processor .

The faster the  processor within the SDR unit, the more bits of data collected gives a better spread of the band in MHz .

3M2  29 continued Recall that this technique is the basis of SDR (software defined radio) receivers.

The technique is the mixing of 2 local oscillator signals,  one with a 90 degree phase change, to produce signals that can be digitally processed by the ADC to create the I and Q signals  to be used in a processor or computer allowing analogue to digital conversion and demodulation and thus output suitable audio and data signals.

3M2  29 continued Recall that these techniques can also be used to create complex modulations for use in transmitters.

The technique of the mixing of 2 local oscillator signal, one with a 90 degree phase change, to create complex modulations for use in transmitters. Such Complex Modulation are, for example, usedin the quadrature phase-shift-keying (QPSK) modulation process, including the I and Q signals as well as the RF carrier signal.