In the previous section we saw that the superheterodyne receiver is suscep- tible to interference from signals on frequencies other than the one we are trying to receive. In this section we see that new interfering signals can be created in the receiver passband because of the inherent nonlinearity of amplifiers and mixers. Also, strong signals outside the IF band of the re- ceiver can reduce sensitivity to desired signals.
Gain compression
All amplifiers have a limit to the strength of the signal they can amplify with constant gain. As the input signal gets stronger, a point is reached where the output doesn’t increase to the same degree as the input; that is, the gain is reduced. A commonly used measure for this property is called the 1 dB compression point. It is shown in Figure 7-6. At the 1 dB point,
the output power is 1 dB less, or .8 times, what it would be if the amplifier remained linear. The 1 dB compression point is a measure of the onset of distortion, since an amplified sine wave does not maintain the perfect sine shape of the input. Recalling studies of Fourier series, we know that a distorted sine wave is composed of the fundamental signal plus harmonic signals.
When a strong input signal outside the IF passband reaches the neigh- borhood of the 1 dB compression point of the input LNA, the gain of the amplifier is reduced along with the amplification of a weak desired signal.
This effect reduces sensitivity in the presence of strong interfering signals.
Thus, in comparing amplifiers and receivers, a higher 1 dB compression point means a larger capability of receiving weak signals in the presence of strong ones. Note that the listed 1 dB compression point may refer to the input or the output. The output 1 dB point is most commonly given, and it is the input 1 dB point plus the gain in dB.
Figure 7-6: 1 dB Compression Point
Third-order intermodulation distortion
A more sensitive indication of signal-handling capability is intermodulation distortion, represented by the third-order intercept. This property is related to the dynamic range of a receiver.
Figure 7-7: Intermodulation Interference
PASSBAND
f1 f2 f0 2f1 – f2 f3 = 2f2 – f1
When there are two or more input signals to an amplifier, the existence of harmonics due to distortion creates signals whose frequencies are the sum and difference of the fundamental signals and their harmonics. If there are two input signals, f1 and f2, and the distortion creates second harmonics, these are the frequencies of the signals at the output of the amplifier:
f1, f2, 2f1, 2f2, | f1 – f2|, 2f1 – f2, 2f2 – f1
If f1 and f2 are fairly close to a received frequency f0 but not in the IF passband, either of the two last terms, 2f1 – f2 and 2f2 – f1, could produce interfering signals closer to f0. This is demonstrated in Figure 7-7. Both f1
and f2 are strong signals outside the IF passband, but they create f3, which interferes with the desired signal f0.
The strength of the interfering signal, f3 in Figure 7-7, increases in proportion to the cube, or third order, of the amplitudes of f1 and f2. The intercept point is the point on a plot of amplifier power output vs. input, expressed in decibels, where the power of f3, the third-order distortion product 2f1 – f2 or 2f2 – f1 at the output of the amplifier, equals the output power that equal amplitude signals f1 or f2 would have if the amplification remained linear. Figure 7-8 shows the amplification curves of f1 or f2, and f3, for a 15-dB gain amplifier. The slope of the f3 curve is three times that of the normal amplification curve. Note that the intercept of the two plots is a graphical point made for convenience. The actual output power in a real amplifier will never reach the intercept point because of the amplitude compression that starts to flatten out the output power at around the 1-dB compression point, which is below the intercept.
Although it doesn’t actually exist in reality, the intercept point is convenient for finding the spurious signal f3 for any strength of f1 and f2. Again, we take the case where f1 and f2 are equal for convenience in mea- surement and quantizing f3, although of course the third degree difference signal will be formed even when they’re not equal. Let’s find the strength of the inband interfering signal f3 when f1 and f2 are –10 dBm at the amplifier output (where the dashed vertical line crosses the linear curve on the figure).
The third-order output intercept, shown in the figure, is 10 dBm, which is 20 dB above the outputs f1 and f2. Since we have noted that the third-order term increases on the dB plot three times as fast as the trouble-causing signals, we find that the output of f3 is +10 dBm – 3 × 20 dBm = –50 dBm (marked by a horizontal dashed line). In Figure 7-8 the amplifier gain is 15 dB and so we see that the inputs of f1 and f2 are –25 dBm, but as shown in Figure 7-7, outside the receiver IF passband. However, the interference
Figure 7-8: 3rd Order Intercept f1 or f2 f3
caused by the intermodulation distortion is the same as an equivalent input for f3, in the receiver passband, of –50 dBm – 15 dBm = –65 dBm. If the data in Figure 7-8 represents the LNA in Figure 7-2, on which we based the sensitivity analysis, and if we are trying to receive a weak signal with this receiver, we can see that the intermodulation distortion in the presence of the interfering signals f1 and f2 makes reading the desired signal impos- sible near, or even tens of dBs above, the calculated sensitivity.
In the example above, we could find the equivalent input power of the
“virtual” interfering signal f3 directly from the distortion curve. Let’s now review the steps to analytically find the third-order term, knowing the intercept point and the input power of the distortion-causing signals.
Remember that we must know whether the intercept point given for an amplifier represents the input or the output (when given for a complete receiver it must be the input). If the output intercept is given, we can always find the input intercept by subtracting the amplifier gain in dB.
If we don’t have the intercept point explicitly from a data sheet, we can use the following rules of thumb to find it and the 1-dB compression point of a bipolar transistor amplifier stage.
Output third-order intercept OIP3 = 10 log (Vce × Ic × 5) dBm (7-6) 1 dB Compression P1dB = OIP3 – 10 dBm (7-7) where Vce is the collector to emitter voltage and Ic is the collector current.
We’ll demonstrate the process of finding the intermodulation distor- tion with an example.
Given: Output third-order intercept point OIP3 = 10 dBm Gain G = 15 dB
Out-of-band interfering signal input power Pi = –40 dBm
Find: Inband equivalent input intermodulation distortion signal power Pim
Step 1: Input intercept point IIP3 = OIP3 – G = 10 – 15 = –5 dBm Step 2: Out-of-band input signal relative to IIP3 = IIP3 – Pi = –5 – (–40) = 35 dB down
Step 3: Inband input IM distortion signal Pim = IIP3 – (3 × 35) = –5 – 105 = –110 dB Simplifying these steps even more, we find:
Pim = 3 × Pi – 2 × IIP3 = 3 × (–40) –2 × (–5) = –110 dBm
In the case of the receiver drawn in Figure 7-2, whose sensitivity was found to be –106.3 dBm, the –40 dBm interfering signals will hardly affect weak signal reception.
Second-order intermodulation distortion
In Table 7-1 we saw that our receiver has a spurious response at 427.65 MHz, which is the desired frequency of 433 MHz less one half the first IF—10.7/2. This response is the difference between the second harmonic of the interfering signal—2 × 427.65—and the second harmonic of the first local oscillator—2 × 422.3—which results in the first IF of 10.7 MHz. These second harmonics are the result of second-order inter- modulation distortion. This spurious response can be reduced by the image rejection filter between the LNA (Figure 7-4) and the first mixer, which should also reject the harmonics produced in the LNA.
Minimum discernable signal (MDS) and dynamic range
We saw that there is a minimum signal strength that a given receiver can detect, and there is also some upper limit to the strength of signals that the receiver can handle without affecting the sensitivity. The range of the signal-handling capability of the receiver is its dynamic range.
The lowest signal level of interest is not the sensitivity, but rather the noise floor, or minimum discernable signal, MDS, as it is often called. This is the signal power that equals the noise power at the entrance to the demodulator. It can be found through Eq. (7-1), minus the last term, S/N.
The reason for using the MDS and not the sensitivity for defining the lower limit of the dynamic range can be appreciated by realizing that
interfering signals smaller than the sensitivity but above the noise floor or MDS, such as those that arise through intermodulation distortion, will prevent the receiver from achieving its best sensitivity.
The upper limit of the dynamic range is commonly taken to be the level of spurious signals that create a third-order interference signal with an equivalent input power equal to the MDS. This is called two-tone dynamic range. It is determined from the input intercept IIP3 with the following relation:
Dynamic range = (2/3) × (IIP3 – MDS) (7-8)
While Eq. (7-8) is the definition preferred by high-level technical publications, you will also see articles where dynamic range is used as the difference between the largest wanted signal that can be demodulated correctly and the receiver sensitivity. This definition doesn’t account for the effect of spurious responses and is less useful than Eq. (7-8). Another way to define dynamic range is to take the upper limit as the 1-dB com- pression point and the lower level as the MDS. This dynamic-range definition emphasizes the onset of desensitization.
It may be called single-tone dynamic range.
The two-tone dynamic range of our receiver in Figure 7-2 using an IIP3 of –5 dBm and MDS of (–106.3 – 8.5) = –114.8 is, from Eq. (7-8)
Dynamic range = (2/3)( –5 – (–114.8)) = 73.2 dB
We note here that the intercept point to use in finding dynamic range is not necessarily that of the LNA, since the determining intercept point may be in the following mixer and not in the LNA. The formula for finding the intercept point of three cascaded stages is
3 2
1 3
2 1 3 1 3
1 3 1
IIP G G IIP
G IIP
IIP = + + ⋅
(7-9) where G1 and G2 are the numerical gains in of the first two stages and IIP31, IIP32, and IIP33 are the numerical input intercepts expressed in milliwatts of the three stages. Then the total input third-order intercept in dBm will be 10log(IIP3).
Note that in calculating IMD of a receiver from its components in the RF chain, you must base the IMD on interfering signals outside of the IF passband and take account of the resulting strength of those interfering signals as they pass through bandpass filters and RF amplifiers.
It should be evident from this description that adding preamplifier gain to improve (reduce) noise figure to increase sensitivity may adversely affect the dynamic range, and using an input attenuator to control
intermodulation distortion and compression will raise the noise figure and reduce sensitivity. The design of a receiver front end must take the con- flicting consequences of different measures into account in order to arrive at the optimum solution for a particular application.
Automatic gain control
Dynamic range is so important in some short-range radio systems that sometimes special measures are taken to improve it. One of them is the incorporation of automatic gain control, AGC. Figure 7-9 shows its prin- ciple of operation.
The incoming signal strength is proportional to the amplitude of the IF signal, which is taken off to a level detector. A low-pass filter averages the level over a time constant considerably larger than the bit time if ASK is used, and longer than short-term radio channel fluctuations if the signal is FSK or PSK. The DC amplifier has a current or voltage output that will control the gain of the LNA and other stages as appropriate to reduce the gain proportionally to the strength of the input signal.
There are some variations to the basic system of Figure 7-9. In one, level detection is taken from the baseband signal after demodulation. For an ASK system, a peak detector with a long time constant compared to the bit time samples the amplitude of demodulated pulses. Also in digital data systems, a keyed AGC implementation is used. Relatively weak signals are unaffected by the AGC, which starts reducing the gain only when the signal strength surpasses a fixed threshold point. Instead of regulating the gain continuously, the gain may be switched to a lower value after the threshold is reached, instead of being adjusted continuously.
While AGC is effective in increasing the single-tone dynamic range, it will not improve two-tone dynamic range when the intermodulation distortion is mainly contributed by the LNA.
Figure 7-9: Automatic Gain Control