Is a pre-amp worthwhile; including step-by-step simplified calculations?

How much improvement may be achieved by fitting a pre-amp and to what effect on the receiver parameters?
The answers to these questions will be different for individual cases. One adds a pre-amp in order to hear weaker signals or work dx further afield. However, whether this purpose is fulfilled will depend upon the existing receiver performance, the station location, the environment and the performance of the pre-amp, eg, noise figure, gain, dynamic range, intermodulation performance, selectivity, etc.
Not all these characteristics are clearly specified or easy to interpret; definitions often vary from vendor to vendor.
As this subject is not covered in Radio HAM examinations, I am attempting to provide some understanding of the effect a pre-amp has on a receiving system. The noise figure is in itself a rather subtle subject which cannot be dealt with in depth in an explanation of this nature. However, some introduction is necessary as noise figure (NF) is generally accepted as the most important single characteristic of any receiving system.
At this stage it seems appropriate to simply and loosely define the terms used.
Definitions

Dynamic range

Is the difference in magnitude (in dB) between the smallest and the largest signals that may be intelligibly resolved (usually without alteration of the attenuator or RF gain controls).
If a small signal and a large signal are present simultaneously then the closer they are together, the more difficult the task of the receiver to discriminate between them. See fig. 1.

FIG 1. Dynamic range display of 90dB (spectrum analyser, frequency domain)

Intermodulation products (IMPs).

When two or more signals simultaneously impinge on a mixer (or any non-linear stage) other signals are produced internally. These signals do not exist outside the receiver and are therefore unreal, but nonetheless may be really troublesome. Suffice to say that these are known as "orders" of intermodulation products, eg third order IMP. The number of the order is determined by the signal and harmonic relationships. The higher the order of IMP, the greater will be the interference to real signals. See fig. 2.

FIG 2. Intermodulation product display in frequency domain (spectrum analyser)

Noise Figure.

This is sometimes called Noise Factor. Perhaps the least understood, and yet believed by most engineers to be the most important characteristic of all when assessing a receiver's performance. Noise figure (NF) is a figure of merit expressed in dB or equivalent degrees Kelvin (K) that tells us how much worse a receiver is than the unachievable and imagined perfect noiseless receiver. Therefore the lower the NF, the more sensitive the receiver is.
The signal to noise ratio at the input to the receiver will be degraded by the noise of the receiver itself; this results in a smaller signal to noise ratio at the output of the receiver, the end to which we wish to listen. A signal only just above the noise at the input may disappear completely into the receiver's noise floor. See the small signal in fig. 1.

Gain.

This is simply the ratio of the magnitudes (expressed in dB) of input to output signals across any device, stage, system or even attenuator; the definition applies to loss as well. It may seem curious that, when adding a pre-amp, it is not necessary to consider the gain of the receiver. However, as will be seen further on, the gain of the pre-amp is very significant indeed.
A signal with noise already on it will arrive at the antenna which is being bombarded with noise from many sources as near and as far as the limits of our imagination and perhaps beyond. The signal and noise is then fed to the pre-amp (and following receiver) via a noisy feeder. The signal, especially a small one, has a great deal of competition before it eventually reaches our ears. See fig. 3.

FIG 3a. Good Signal to noise ratio (in time domain, oscilloscope)

FIG 3b. Poor Signal to noise ratio (in time domain, oscilloscope)

Before moving on, let's summarise the situation so far:

1. When the receiver is switched on it will produce noise, even without any input connection whatsoever. In fact, with an impossible noiseless termination at the antenna input socket, the receiver will still produce noise.

2. Any signal received must, in order to be resolved, be of greater amplitude than all the combined noises with which it competes. In modern times computer enhancement helps to achieve this in difficult cases (at processing stage).

3. If strong signals cause the receiver to produce IMPs, the wanted signal may be masked by them or unreadable. This is one form of "overload".

4. The dynamic range of the receiver stretches from its "noise floor" to its overload or "ceiling".

A pre-amplifier can improve dx capability by improving sensitivity (noise figure) but only at some cost to other parameters.

Sensitivity.

This is the lowest level at which a weak signal may be received intelligibly. A receiver with good sensitivity will receive weak signals and will have a low noise floor (or low NF). Receivers have different sensitivities according to band, mode, age, alignment, state of the art at time of design, price, manufacturer and other variables.
The main reason for adding a pre-amp is to effectively reduce the NF of the total receiving system. In fact, as will soon become apparent, the noise figure of the receiver plus pre-amp is very little higher than the NF of the pre-amp alone. Therefore, the poorer the sensitivity of the receiver, the greater could be the improvement of small signal reception by adding a pre-amp.

Consider the following three cases:

1. Operator A who has an ageing two metre rig with a 10dB NF. He/she only has local QSOs.

Operator B has a two metre rig with a 6dB NF. He/she only has local QSOs but works further afield than operator A; and works some dx occasionally too.

Operator C owns a super new all-singing, all-dancing multimode two metre rig fully equipped with bells, buzzers, flashing lights and with a NF of only 3dB and works lots of dx.

All three operators run similar antenna systems, feeders, cable lengths and share the same QTH (very hypothetical). Only the rigs differ as above.

Each operator now tries the same pre-amp to see whether it improves their systems
performance.

Assume the pre-amp has typical characteristics, eg gain = 20dB (ratio 100:1) and NF = 1.5dB.
It now becomes necessary to introduce a simple algebraic formula in order to calculate the effect that the pre-amp will have on each rig. If you cannot follow it, don't worry but read the text that goes with it and refer to Fig 4, a chart that will help with the calculations.

Ft = Fa + ((Fr - 1) / Ga)

when:
Ft = total NF (Rx plus pre-amp)
Fa = pre-amp NF
Ga = pre-amp gain
Fr = Receiver noise figure.

There is no need to consider the receiver gain Gr, so it does not appear in the formula. No account has been made of the antenna and feeder NF, although it is very significant to the station performance. The measurement would be a little more complex and probably not contribute very much to the point of this particular explanation that is concerned with the pre-amp. All the ratios in dB must be converted to numerical ratios when making the calculation, the result then being converted back to dB NF. See fig. 4. Inter-connection losses have not been considered here though they can be very significant.

If a similar experiment is carried out with a pre-amp of 1.5dB NF and 10dB gain (ratio 10:1) the result would be as follows:

Operator A:

1.413 + ((10 - 1) / 10) = 2.313, NF = 3.641dB

Operator B:

1.413 + ((4 - 1) / 10) = 1.746, NF = 2.42dB

Operator C:

1.413 + ((2 - 1) / 10) = 1. 513, NF = 1.798dB

In the above three cases, the Noise Figures all end up larger with a 10dB gain pre-amp than with a 20dB gain pre-amp. More gain results in lower noise figure.

Do the exercise once more using a pre-amp with 1.5dB NF and 30dB gain (ratio 1000:1).

Operator A:

1.413 + ((10 - 1) / 1000) = 1.422, NF = 1.529dB

Operator B:

1.413 + ((4 - 1) / 1000) = 1.416, NF = 1.511dB

Operator C:

1.413 + ((2 - 1) / 1000) = 1.414, NF = 1.504dB

Two significant points emerge from the high gain example: all three noise figures are virtually the same (or differ insignificantly), and all three noise figures are only fractionally higher than the noise figure of the pre-amp alone.
It may seem surprising to some that an old 'noisy' receiver with a pre-amp can be just as sensitive as a new "quiet" receiver with pre-amp. However it is so.
Another surprise may be that the RF gain of the receiver may be backed off considerably without any loss of sensitivity but considerable reduction of Rx noise. One should experiment with the pre-amp and Rx gain control (even the Rx attenuator) for the most suitable setting for each band and indeed, each signal. Remember, the receiver gain Gr does not appear in the formula: Ft = Fa + ((Fr - 1) / Ga).

How often one hears an operator give a signal report "You're an S8 on my meter but I've switched on a pre-amp and have a permanent noise level of S5." By reducing the RF gain control of the receiver the S-meter may possibly be set to a fixed level when under no signal conditions. The calibrations will almost certainly not follow the original AGC law, but at least it will have some relative use (which is all an S-meter has anyway!). And the background noise in the loudspeaker will not appear abnormally high. It is possible to put attenuation between the pre-amp and receiver to minimise or eliminate receiver overload. It is even possible to control the pre-amp with a form of AGC. One could also calibrate the S-meter, but all these things are beyond the scope of this article. However, it may be seen that the action of the pre-amp is to deliver to the receiver a signal that is sufficiently above the receiver's noise level to be suitably detected and processed.
Such a system produces excellent results when the station is in a 'quiet' radio environment, free of other relatively close or strong transmissions; that proviso is the major drawback of a pre-amp. Although it is very good at small signal handling, it can suffer considerably from the effects of strong signals which either overload the pre-amp or cause the pre-amp to overload the front end of the receiver.
If the receiver has a dynamic range of say 90dB (1,000,000,000 to 1) with a noise floor of minus 110dBm, then the maximum signal it can handle will be -20dBm. Adding a pre-amp that drops the noise floor by say 10dB to -120dBm will also drop the ceiling by 10dB to -30dBm (assuming sufficient dynamic range of the pre-amp). If signals larger than - 5OdBm are presented to a pre-amp with 20dB gain, the receiver will overload, producing IMPs and other unwanted effects. See fig. 2.

So, a pre-amp would not be a lot of use to a station well located atop an exposed hill, surrounded by other ham stations, radio taxi bases, fire, police and ambulance stations, a local broadcast repeater, microwave food processing factory, and for good measure, an international airport thrown in. The solution here would be to have a switchable pre-amp (if at all).
The task of the receiver designer is to offer optimum performance, suitable for most users, uses and situations likely to be encountered and maximum sales. Fitting a pre-amp becomes more of a special application, for better dx hunting or improving a station in a 'black hole' location.
The state of the art at present is not such as to permit the design of receivers with very low noise floors and wide dynamic ranges and superb IMP performance, all at an affordable, price. The motor industry has an analogous problem. It can build a car that will travel at 200mph or achieve 90mpg but not both at the same time. Receivers can be produced to operate very well indeed under certain conditions, but only at the sacrifice of performance in other parameters. Like most things, they are a compromise. That is why a pre-amp can be a very useful addition to a station but only in an appropriate situation.

The pre-amp is most effective at the mast head because it can present a good signal to noise ratio to the feeder which is itself lossy and noisy. The signal the antenna offers to the feeder is better than the signal the feeder offers to the receiver, therefore the larger the signal to noise ratio at the antenna end of the feeder, the less noise the receiver has to overcome.
I believe that I previously operated from a "black hole" location: 200 feet below the top on an ironstone hill surrounding the QTH on three sides. The fitting of a cheap but good pre-amp (costing just a few pounds) transformed the station. However, it must be stated that this particular 'black hole', down in a dip, is very free of interfering signals.
Pre-amps seem to be most useful above frequencies of about 4 mHz.but this bfigure is not cast in stone. Ambient and atmospheric noise below about 4 mHz limits the usefulness of pre-amps. HF rigs with switchable pre-amps seem perfectly satisfactory without the pre-amp at low frequencies (say top band) and meet all dx conditions if a good antenna is used of course.
It is worthy of mention that many years ago professional communicators learned that money spent on improving their station was much more effectively put into the receiver than the transmitter. "You've got to here 'em to work 'em". Massive increases in transmit power (and cost) are necessary to achieve small increases in range. Small improvements to a receiver front end can extend range considerably. Radio Astronomers, for example, use cryogenically cooled pre-amps of exceptionally low NF, specified in degrees Kelvin for ease of numbers. Constructors should line up their pre-amps for minimum noise figure rather than maximum gain, the former being more important. Manufacturers optimise noise performance and then just measure the gain to ensure that it meets specification.
For in depth understanding of noise figure I recommend Noise Performance Factors in Communications Systems by W W Mumford and E H Scheibe, Published by Horizon House - Microwave Inc. Dedham, Massachusetts.

Rod, G4TUG