Chapter 23: Receiver Fundamentals

Its signal-to-noise ratio

Readability depends on how far a signal stands above the noise: its SNR. A strong signal on a band that is noisier still is no easier to read, and more volume raises the noise too.

3 dB

(S + N) ÷ N = (1 + 1) ÷ 1 = 2, and 10 log 2 = 3 dB. S ÷ N alone gives 1, or 0 dB; the manual’s ratio also counts the noise on the top line.

30 dB

The ratio is about 1 000 (strictly (400 + 0,4) ÷ 0,4 = 1 001), and 10 log 1 000 = 30 dB. Dividing the noise by the signal turns the ratio upside down and gives −30 dB.

Everything except the wanted signal, other stations too

N covers everything except the signal wanted: noise from the receiver, noise picked up from the band and even other stations. Leaving other stations out is the usual slip; to a receiver they are noise too.

The random motion of electrons inside them

Electrons in a semiconductor move about semi-randomly, more so as it gets hotter, so this noise rises with temperature. Phase jitter in a synthesiser’s VCO gives phase noise, a different source.

Boltzmann’s constant

In PN = kTB, k is Boltzmann’s constant (about 1,38 × 10⁻²³ J/K), T the noise temperature in kelvin and B the bandwidth in hertz. The bandwidth has a letter of its own, B.

10 dB less

Thermal noise power is in proportion to bandwidth, so a tenth of the bandwidth gives a tenth of the noise: 10 log 10 = 10 dB less. It depends on bandwidth as well as temperature, so it does change.

7 dB less

The bandwidth falls 2 700 ÷ 500 = 5,4 times, and so does the noise power: 10 log 5,4 = 7,3 dB less, nearest 7 dB less. Noise follows bandwidth, so it cannot stay unchanged.

Their thermal noise falls as they get colder

Thermal noise power is in proportion to temperature, so a colder input stage adds less noise, which matters most at VHF and above. Drift is a stability matter; these stages are cooled for low noise.

Jitter in the voltage-controlled oscillator of their PLL

Phase noise came from jitter in the VCO of the synthesiser’s phase-locked loop; like thermal noise, it grows with bandwidth. Random electron motion is the cause of thermal noise instead.

Distant thunderstorms

Atmospheric noise is the crackle of distant thunderstorms, a problem mostly on the low bands. Noise from the sun and stars, which the manual groups as galactic noise, arrives mainly at VHF and above.

Power supplies for LED lighting

LED lighting power supplies switch rapidly and can swamp signals in towns, adding to the noise from power lines, ignition systems and motors. A plain filament bulb has nothing switching inside it to make noise.

The sun

The manual names the sun, the strongest single radio noise source in the sky: aim a beam at it and the noise on VHF and UHF rises sharply. The Moon gives off only a little noise.

The ionosphere stops it below the critical frequency

Galactic noise must pass through the ionosphere, which turns back frequencies below the critical frequency, so little of it arrives on the lower HF bands. The sources themselves radiate at the lower frequencies too.

Atmospheric noise

Up to about 30 MHz atmospheric noise from thunderstorms predominates, though in towns electrical noise may take over. Galactic noise mostly matters at VHF and above, as the ionosphere keeps it out on HF.

Your receiving set-up is working well

Galactic noise is fairly weak, so a system that can hear it is quiet and sensitive. Only the sun is strong: aim a beam straight at it and you should hear plenty of noise.

On HF, band noise is well above the receiver’s own noise

At HF and below, noise picked up from the band swamps the receiver’s own noise; from VHF up, the receiver’s noise becomes the limit. Saying the same of UHF gets it the wrong way round.

Save your money: on 40 m the band noise already far exceeds the receiver’s own noise

On HF, and above all on the low bands, the band noise is far above the receiver’s own noise, so a quieter preamp leaves the signal-to-noise ratio unchanged. It would pay off at VHF and above.

A very low noise temperature

At UHF the receiver’s own noise limits weak-signal reception, so a low noise temperature counts most, with low-noise preamplifiers and low-loss feed lines. Dynamic range matters when strong signals are near.

Decibels (dB)

The manual gives the noise figure in dB; a noise temperature in kelvin carries the same information, hence the usual mix-up. Microvolts and hertz measure a signal level and a frequency.

Its actual noise power can then be worked out simply

With a noise temperature, PN = kTB gives the noise power in whatever bandwidth is used, ready to compare with the signal. It is an effective figure, not the temperature of the case.

6 dB

Noise power is in proportion to the noise temperature, so a quarter of the temperature gives a quarter of the power: 10 log 4 = 6 dB less. 12 dB would apply 20 log, the voltage formula, to a power ratio.

None at all, at that temperature

At 0 K there is no thermal motion, so PN = kTB comes to zero: no thermal noise at all. Every temperature above absolute zero gives some noise, but 0 K gives none.

100 K

A kelvin is the same size as a degree Celsius, and 0 °C = 273 K, so −173 °C = −173 + 273 = 100 K. Adding 173 to 273 gives 446 K, hotter than boiling water.

300 K

Room temperature is about 27 °C, and 27 + 273 = 300 K. 273 K is 0 °C, where water freezes, and 27 K forgets to add the 273.

Selectivity

Selectivity is telling apart signals close together in frequency and passing only the one wanted; it depends mostly on bandwidth. Sensitivity concerns hearing weak signals, not separating them.

Sensitivity

Sensitivity is how well a receiver hears very weak signals, such as those from distant low-power stations. Selectivity is a different quality: separating signals that are close together in frequency.

Sensitivity

A signal level in microvolts needed for a stated signal-to-noise ratio is a sensitivity figure; the bandwidth is quoted because noise depends on it. Selectivity would be given as a bandwidth or a rejection.

Its range of signal strengths, weak to strong, handled at once

Dynamic range is the spread of signal strengths handled together: a weak signal received despite much stronger ones nearby, stated in dB with their spacing. The span of frequencies tuned is the tuning range.

The further off a strong signal is, the more of it can be tolerated

The further an interfering signal is from the wanted one, the more of it the receiver can tolerate, so a dynamic range in dB means little without the spacing. Closer signals are harder to cope with, not easier.

105 dB

The stronger signal is −20 − (−125) = 105 dB above the weaker, so the receiver needs 105 dB of dynamic range at 5 kHz spacing. Adding 125 and 20 to get 145 dB mishandles the minus signs.

A local signal may be 90 dB stronger than a weak one a few kHz away

A typical weak signal may arrive at −120 dBm and a strong local one at −30 dBm, 90 dB more, a few kilohertz away, and the weak one must still be heard. Signals on exactly one frequency would defeat any receiver.

3 × 10⁷

−40 − (−115) = 75 dB, and 75 dB = 70 + 5 dB: 10⁷ × 3,16 ≈ 3,2 × 10⁷, nearest 3 × 10⁷. As a voltage ratio, 75 dB would be only about 5 600.

10⁻¹³ W

A level of −100 dBm is 100 dB below 1 mW: 10⁻³ W × 10⁻¹⁰ = 10⁻¹³ W, a tenth of a picowatt. Reading it as dBW, 100 dB below 1 W, gives 10⁻¹⁰ W, a thousand times too much.

−120 dBm

P = V² ÷ R = (0,3 × 10⁻⁶)² ÷ 50 = 1,8 × 10⁻¹⁵ W, which is −117 dBm, nearest −120 dBm. Leaving out the 50 Ω gives 9 × 10⁻¹⁴ W, about −100 dBm.

Its bandwidth

This is selectivity, which the manual says is set mostly by the bandwidth, given in hertz: the narrower it is, the fewer neighbouring signals get through. More gain only amplifies the neighbours too.

About 100 to 200 Hz

When propagation is good the bands get crowded, and in a CW contest signals may sit only 100 to 200 Hz apart. That is why the manual puts selectivity first among a receiver’s needs.

A tuned radio frequency (TRF) receiver

Filtering and amplifying at the signal’s own frequency, then rectifying the AM, is the TRF receiver. A superhet first converts the signal to an intermediate frequency and does its main filtering there.

It rectifies the AM signal to recover the audio

That block is the detector, a half-wave rectifier that demodulates the AM signal. A TRF receiver has no frequency conversion at all; it filters, amplifies and detects at the signal’s own frequency.

The two filters are tuned together by one control

The arrows mark the filters as tunable, and the broken line means they are ganged, so a single control tunes both. The regeneration path is the solid line looping back to the RF amplifier’s input.

Feeding some of the RF amplifier’s output back to its input so that it adds to the signal

Regeneration is positive feedback: part of the output returns to the input in step with the signal and reinforces it, so the signal is amplified again and again. Feedback that opposes the signal is negative and lowers the gain.

It raises the gain and sharpens the selectivity

The signal circulates through the RF amplifier and its filter many times, amplified and filtered again on each pass: more gain and sharper selectivity together. It does not broaden the selectivity.

The RF amplifier breaks into oscillation

Positive feedback turns an amplifier into an oscillator, so past a certain point the regenerative stage oscillates by itself. Up to that point its gain rises; the gain does not collapse.

Just short of the point where it oscillates

It is set for the most sensitivity and selectivity without oscillation, just below the threshold. Just past it, barely oscillating, is the setting used for CW and SSB, not for AM.

By setting the regeneration so that the circuit just oscillates

Set so that it just oscillates, the stage beats with CW and SSB signals to make them audible, though adjustment is tricky and quality poor. Just short of oscillation suits AM, which brings its own carrier.

To make the receiver more sensitive

The RF stage lifts the weak signals from the antenna so that fainter stations can be heard: it improves sensitivity. Selectivity comes mainly from filters and bandwidth, though tuned circuits around the stage help a little.

It is simple to build and needs only a few parts

A TRF receiver can be built with two or three transistors and few other parts, which mattered when tubes were costly. Audio quality is not its strength: its poor selectivity lets neighbouring signals in.

Tubes were costly, so every one saved counted

Each tube was costly, so a design needing only a few amplifying stages kept the price down. Tubes amplified radio frequencies perfectly well; TRF receivers of that era used them at RF.

Very poor selectivity and dynamic range

Tunable RF filters cannot reject a signal only a couple of kilohertz away, so unwanted signals reach the detector or cause intermodulation. Images belong to the direct-conversion receiver; a TRF has no local oscillator at all.

The received signal and the local oscillator

The product detector mixes the incoming signal with the tunable LO, which the manual also calls the BFO, and the difference lands at audio. A direct-conversion receiver has no intermediate frequency; that belongs to the superhet.

To keep out broadcast and other out-of-band signals

Its job is only to block strong interference from outside the band, such as local broadcast stations; the selectivity comes later, from the audio lowpass filter. That is why one fixed filter can cover a whole band.

No: one fixed filter covering the whole band will do

The input filter only keeps out strong signals well away from the band, so a fixed filter for the whole amateur band is enough. Tracking tunable filters are what a TRF needs, since they give its selectivity.

Essentially one circuit, named for the job it is doing

The three names describe essentially the same circuit, chosen by the role it plays; the DC receiver’s product detector is drawn with the mixer symbol, a circle with a cross. One such circuit does the job there.

Where its carrier would have been, had it been sent

An SSB signal is named by its pseudo-carrier frequency, where the suppressed carrier would have been; a USB signal then extends 300 Hz to 3 kHz above it. The centre of the sideband is not the quoted frequency.

14 250,0 kHz

The LO goes where the suppressed carrier would be, 300 Hz below the lowest component: 14 250,0 kHz, giving audio from 300 Hz to 3 kHz. At 14 250,3 kHz every tone comes out 300 Hz low.

Just below 7 500 kHz

The LSB lies just below 3 750 kHz, so adding the LO puts the sum just below 7 500 kHz, as the manual’s LSB graph shows. Just above is the USB case; 300 Hz to 3 kHz is the difference.

In the same place as for the USB signal

For USB and LSB alike, the LO goes where the suppressed carrier would be and recovers the audio; only the side on which the sideband lies differs. An LO 3 kHz lower would turn the audio upside down.

Inverts it, undoing the inversion made at the transmitter

Making an LSB signal inverts the audio spectrum; mixing it down with the LO inverts it once more, so the audio comes out the right way round. Nothing later has to turn it round again.

7 024,3 kHz

The tone is the difference between signal and LO, so the LO goes 700 Hz away: 7 025,0 − 0,7 = 7 024,3 kHz (7 025,7 kHz works too). On 7 025,0 kHz the LO zero-beats the signal, giving no tone.

800 Hz

The audio is the difference between signal and LO: 10 120,8 − 10 120,0 = 0,8 kHz, an 800 Hz tone. 8 kHz misplaces the decimal comma, and the 20 240,8 kHz sum product is far above audio.

The audio lowpass filter after the mixer

Unwanted nearby signals become audio tones above the speech band, and the lowpass filter after the mixer removes them, so the selectivity is far better than a TRF’s. The input filter only blocks strong out-of-band signals.

So that strong signals cannot overload the mixer

A strong signal easily overloads a mixer, causing intermodulation distortion, so little gain goes ahead of it and most is placed at audio, after the lowpass filter. Low RF gain does not lower the receiver’s noise.

In the audio amplifiers after the lowpass filter

Gain ahead of the mixer is kept low so that strong signals cannot overload it, so most of the amplification is done at audio frequency, once the lowpass filter has removed unwanted signals.

AGC

Automatic gain control (AGC) cuts the gain as signals get stronger and restores it for weak ones, keeping the output level fairly steady. ALC, automatic level control, does a similar job in a transmitter.

Resetting the gain as signals differ in strength and fade

Signals vary widely and fade with propagation, so a manual gain control would need constant work, blasting the ear on loud signals and missing weak ones. Frequency drift is a stability matter, not a gain one.

The weak one can be missed unless the gain is raised again first

Turned down for the strong signal, the gain stays low, so a weak one can pass unheard until it is raised; a painful blast is the opposite case, tuning from weak to strong. AGC handles both.

The RF amplifier and the first audio amplifier

The AGC control voltage acts on the RF amplifier and the first audio amplifier, keeping the output fairly constant. Acting on the final power amplifier alone would leave the earlier stages free to overload.

From the audio, just after the first audio amplifier

It samples the audio after the first audio amplifier, so this AGC is audio-derived. It does not sample RF before the mixer; a superhet, in the next chapter, takes its AGC from the IF.

The RF gain control

The RF gain sets how much the incoming signal is amplified ahead of the mixer, and so how weak a signal can be brought up; turning it down trades sensitivity for less overload. Volume only changes loudness after detection.

The relative strength of the received signal

Usually driven by the AGC voltage, the S meter shows signal strength on a rough scale from S1, very weak, to S9, very strong. It is seldom well calibrated, so its readings are relative; SWR needs its own meter.

12 µV

Each S unit is about 6 dB, a voltage ratio of 2, so S6 is 18 dB down: 100 ÷ 8 = 12,5 µV, nearest 12 µV. Using the power ratio, 4 per S unit, gives 1,6 µV.

1 000 times

Five S units of about 6 dB each make 30 dB, and 30 dB is a power ratio of 1 000. Reading 30 dB as 30 times treats decibels as a plain ratio.

Only roughly, as most S meters are poorly calibrated

An S meter is a rough guide: the manual warns that S meters are seldom well calibrated, and its S9 of 100 µV is not universal (the IARU uses 50 µV on HF).

You just tune it in; there is no regeneration control to set

The DC receiver’s own LO beats with the signal, so SSB and CW are simply tuned in; a regenerative set must be made to just oscillate, which is tricky. The same LO, also called the BFO, does the whole job.

It cannot reject images on the far side of the LO

A signal beyond the LO, where the opposite sideband would lie, is converted to audio as well and cannot be filtered out. Poor selectivity is the TRF’s weakness; the DC receiver’s is very good.

It is an image, which this receiver cannot reject

The CW signal is 1,2 kHz below the LO, where an LSB signal would sit, so it becomes a 1,2 kHz tone in the speech band: an image. The LO has not moved.

By using a more complex design than the basic one

More sophisticated direct-conversion designs can reject images, but they are complex and outside the course. A narrower audio filter cannot help, because the image’s audio lies in the same range as the wanted audio.

Otherwise some of it is radiated and interferes with other listeners

A DC receiver’s LO sits at or very near the reception frequency, so any that leaks to the antenna is radiated and interferes with nearby listeners. The LO feeds the mixer directly; isolation is about radiation, not drive.