The capabilities of an information processing or collecting system depend upon its sensitivity, its bandwidth, and its noise level. For a heterodyne receiver the signal bandwidth is usually set by the choice of RF & IF filters. In this section we will examine the factors which affect the receiver's sensitivity and noise performance. Although the following analysis uses the example of a photoconductive detector it is worth bearing in mind that similar results can be obtained for diode mixers and also for bolometric power detectors. Hence the conclusions of this section are true for many types of signal detection and measurement system.
2.1 Conversion Gain.
Part 1 showed that a heterodyne mixer could be expected to produce an output IF current (with the DC filtered off) of
when provided with a single frequency input signal, and pumped or driven with an LO input, . The mean IF power the mixer supplies to the following amplifier whose input resistance is R will therefore be
where the angle brackets, , indicate a time-averaged value. Since we can therefore say that
In a similar way we can say that the signal and LO powers falling on the mixer will be
combining these we can say that
When using a specific LO power level we can define a Conversion Gain, of value
which we can use to rewrite expression 2.6 in the form
Looking at this result we can see that 2.8 shows that the IF power level is proportional to the input signal power level. The value of the conversion gain essentially determines how much IF power we get from a given input signal level.
The above argument indicates that the conversion gain value is proportional to the LO power level and the IF amplifier's input resistance. This implies that we could obtain as high an output IF level as we might like by increasing the LO power and/or amplifier resistance. In practice there are two reasons why this isn't always true:
Firstly, the above analysis assumes that each of the incoming stream of signal & LO photons have a chance, , of transferring their energy to an orbiting electron, converting it into a free one. However, the number of electrons inside the mixer is finite. As a result, if we keep increasing the rate at which photons arrive we'll eventually begin to ‘run out’ of available electrons. As this happens, the chance of an extra photon producing a new freed electron will reduce. Hence the detector's quantum efficiency, , tends to fall once the signal+LO level goes above some finite value. Secondly, we have to maintain an electric field across the detector in order to ‘sweep out’ the liberated electrons and get a measurable current. This field is created by the applied bias voltage. However, looking at figure 1.3 we can see that this bias is applied to the detector and the amplifier's input resistance in series. As a result, the actual voltage across the detector will be . where i is the current through the detector (including both the IF and the DC contributions). The above analysis actually assumes that . Making R (or i) too large has the effect of reducing the bias field across the detector, hence reducing the current level produced by a given signal+LO power.
For the above reasons (and some others we haven't mentioned) the expression 2.7 is only reliable when the the input signal+LO power level, amplifier resistance, and output current are ‘small’ — i.e. low enough not to disturb the assumptions mentioned above. At higher levels the conversion gain value tends to saturate — i.e. stop increasing with power/resistance. Any further increase in the input power or amplifier resistance then causes the gain to fall. As a result, there is always an optimum LO power level and amplifier resistance which gives the highest possible conversion gain. The precise details of these values will depend upon the actual detector.
The conversion gain, G, is one of the standard values which tend to be measured and quoted to indicate the performance of a heterodyne or superheterodyne receiver system. G is called a ‘gain’ because it is a ratio of an output power to an input power. In most practical cases the actual output power is smaller than the input, so it would be more honest to call it a ‘loss’! Despite this, the convention is to call it a gain — even if it is a gain of -10dB's, i.e. the output is ten times smaller than the input! It is called a ‘conversion’ gain because it indicates the relative level of an output which has been converted to a frequency which differs from that of the input.
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