Circular polarisation using crossed dipoles feeding a quadrature hybrid
Some initial conditions:
A signal arriving at the dish will induce voltages in the two antenna pairs that have amplitudes that depend not only on the strength of the incoming signal, but also on the angular position of each antenna relative to the signals E field. Being angularly displaced by 90 degrees, when one pair is orientated to receive maximum signal, the other will be in a null, and receive nothing. A 45 degree shift from this condition would result in equal amplitudes at the two antennas (though the one that had previously received a maximum, would now have an amplitude of only 70.7% of its previous value).
In the case of a signal of fixed (ie, plane) polarisation, the signals at the two antennas will be either exactly in phase or exactly out of phase with each, again, depending on their positions relative to the plane of the incoming signals E plane.
An interesting (and potentially useful) situation arises if the plain of the incoming signal is not fixed, but is rotating – particularly if it is rotating at a rate of 360 degrees per rf cycle (a property that is easy to achieve). At insignificantly slow rotational speeds, measured in terms of seconds, minutes or hours (which often occur in non terrestrial propagation paths [Faraday rotation, for example]), the signals from the two antennas remain purely in or out of phase with each other.
[In this situation, a system that used plain polarisation would have to have the ability to rotate either the transmitting or receiving antenna to keep signals at a maximum – and a method of monitoring and making that change. Circular polarisation is free from this restraint]
As the speed of rotation begins to approach that of the signal’s change of phase within its rf cycle, the phase relationship of the two signals from the two antennas begins to be moved from the purely in or out of phase condition. By the time the speed of rotation is 360 degrees per rf cycle (an easy condition to achieve in practice), the offset will have increased to 90 degrees. This is an easy situation to visualise. Consider a moment in time when the signal at one antenna is both in exactly the right plain for a maximum coupling, and is also at a maximum in the rf cycle. A further 90 degrees on in the electrical cycle, the signal will also have rotated 90 degrees – just the right amount to induce a maximum at the other antenna.
Adding the quadrature Hybrid
Knowing that the signals at the two antennas will be 90 degree phase shifted, means that they arrive at the Hybrid H and V ports with a 90 degree phase shift also. Whether V leads or lags H by 90 degrees depends on which hand the signal is (ie, left hand or right hand) – and this leading or lagging state makes all the difference as to which output port it will appear at the Hybrid (or rather, at which port the addition of the signals from the two inputs will be constructive, and at which they will be subtractive)
Consider the situation when the signal at V peaks 90 degrees after it does at H:
At a time when V is at its + peak, H is 90 degrees ahead, and therefor is at zero. Each of the Hybrid arms are an electrical 90 degrees, so at output A consists of a + peak from H (because its 90 degrees ahead ) and a zero from H ( because its 180 degrees ahead, but H, unlike V, started at a zero) – the combination of the two signals obviously will be zero also.
Similarly, 180 degrees later, at a time when V is at zero, the V originated signal at output A will be 90 degrees ahead (ie, be at + max). At this same instant in time, H will be at its – peak (it is lagging V by 90 degrees), so the H originated signal at output A will be
For these two examples, signals from inputs V and H have arrived at output A exactly in phase. In fact, no matter what the starting point is chosen to be, this in-phase condition will hold. The signal at output A is the fully constructive addition of inputs V and H.
Using the same starting points to establish how the signals appear at output B, will show that they arrive this time in the out-of-phase condition, always resulting in complete cancellation.
Thus, all of the signal arriving at the antenna has appeared at the A output.
Considering the opposite hand of polarisation (ie, V peaks 90 degrees before it does at H):
Working through the previous examples, but with V leading H, rather than lagging by 90 degrees, will show similar constructive and destructive additions at the two output ports. This time, however, constructive addition will occur at the B port. So now, all the signal from the antenna will appear there.