Amateur Bands: A Top to Ten TRF

Since the mid-1930's — because of its far superior selectivity — the super-heterodyne principle has been the de-facto standard for practically all radio receivers. In certain very specific situations, however, the simplicity and passiveness of the TRF has distinct advantages.

A super-heterodyne receiver contains an internal oscillator. This can introduce noise to the incoming signal and also cause the receiver to radiate a small signal, which could interfere with other equipment. A super-heterodyne is also vulnerable to strong "image" signals on the other side of the IFO (intermediate frequency off-set) oscillator. Weaker images can even occur at off-sets corresponding to multiples [or harmonics] of the IFO oscillator frequency.

There are also inherent tracking errors between the IFO oscillator and the received pass-band centre, which can effectively shift the resulting intermediate frequency, thereby attenuating signals differently at different parts of the tuning range. For higher frequencies, double conversion super-heterodynes are necessary, which can augment the tracking error and noise problems.

The use of an IF off-set beat-frequency oscillator [BFO], for hearing keyed carrier Morse Code transmissions, introduces yet more noise and can generate spurious harmonics between the BFO and the IFO oscillator.

A tuned radio frequency [TRF] receiver, on the other hand, is entirely passive in operation. It does not, within itself, generate any radio-frequency signals. It is there­fore much quieter [generates less spurious noise] than a super-heterodyne and tracking errors cannot exist. I have therefore opted for the much simpler TRF de­sign. Selectivity and audio shaping will be done using a comprehensive audio filter placed between the receiver's audio output and the final audio amplifier.

A variable capacitor with a capacitance ratio 3:4 facilitates a frequency ratio [bet­ween the bottom of its tuning range and the top of its tuning range] of about 1·15. Consequently, the ratio between the pass-band width at the low end of its tuning range and the pass-band width at the high end of its tuning range is also 1·15. So, if the pass-band at the low end of its tuning range be 10 kHz wide, then the pass-band at the high end of its tuning range will be 11·5 kHz wide. A constant pass-band width, of up to 10 kHz, for the receiver, across the whole of its tuning range, can easily be determined by a subsequent audio filter.

With this regime, a straight-forward TRF receiver can be more than adequately sel­ective for use on any of the amateur bands from Top to Ten. It renders the use of the super-heterodyne principle unnecessary.

A block diagram of the basic TRF receiver is shown below. The red line marks the boundary between what I call the Front End and what I call the Back End. The Front End deals with the RF signal up to its detection: the extraction of the audio content. The Back End deals with shaping and amplifying the audio content. I propose that there be a separate instance of the Front End for each of the Amateur Bands, which share, in turn, a single instance of the Back End. Different Front Ends may contain different numbers of RF stages to achieve necessary RF selectivity.

Schematic of the Top to Ten TRF (Tuned Radio Frequency) receiver.

The Front End

A more detailed schematic of the Front End is shown below. Each RF resonator (pick-up or tuning coil with its respective variable capacitor) is electrically isolated. It is coupled only inductively to the rest of the receiver. In the case of the pick-up coil, the signal is picked up from the resonator by a single turn of Litz wire wound on one end of the coil former. Each tuning coil has a loop comprising a few turns of wire wound at each end of the main resonator coil. One loop is to allow the input signal to energize the resonator. The other is to pick up the output signal from the reson­ator.

More detailed schematic of the RF section of the Top to Ten TRF receiver.

An RF amplifier then strengthens the signal and passes it to the next resonator. I have shown only two resonator stages. More can be added as required to achieve the desired pass-band width at the low-frequency end of the tuning range. Reson­ator stages are added by repeating the detail within the red rectangle above. The resonators of the different stages can be off-set one side or the other of the pick-up resonator's frequency in order to flatten the top of the pass-band profile. The final resonator feeds the signal to the demodulator.

Schematic of the inductive demodulator of the Top to Ten TRF receiver. The demodulator extracts the audio frequency content of the original RF signal. The RF signal is taken from the final RF resonator via a small in­ductive coupling coil comprising a few turns of Litz wire wound at one end. The coupling coil is earthed at its mid point to provide a balanced source. Opposing diodes separate the +ve and −ve halves of the RF signal. Their outputs are fed to the balanced input of an audio trans­former with a centre-tapped primary. The induct­ance of the audio transformer's primary winding is well high enough to block the RF components of the signal, thus allowing only the audio con­tent to pass through to the output winding.

I prefer the centre-tapped transformer configuration with just two diodes because this allows both the radio and audio frequency signals to be balanced with respect to chassis potential (earth or ground). Impedance calculations should take account that each half-cycle at radio frequency uses only half of the radio frequency coupling coil's winding and that likewise, each half-cycle at audio frequency uses only half of the primary winding of the audio transformer. I also prefer to earth (ground) the centre tap of the audio transformer output winding to balance the audio signal with respect to chassis, thus minimizing its susceptibility to electrical interference on its way to the receiver's Back End, which is in a separate cabinet.

If amplification is necessary at this stage, the opposing diodes could be replaced by op-amps configured for +ve and −ve inputs and outputs respectively. Forming a Morse Code tone from a keyed continuous wave transmission or reconstituting the speech from a single-sideband transmission is done later in the Back End of the receiver. I think it must be nostalgia that makes me yearn to implement the RF am­plifiers herein using electro-thermionic triodes. Notwithstanding, I think I will always end up using packaged op-amps.

The Back End

There is a separate Front End for each radio band. These all share just one Back End. A block schematic of the Back End is shown below.

Schematic of the highly selective audio filter of the Top to Ten TRF receiver.

The Back End receives, from the Front End to which it is currently connected, a bal­anced audio signal. Because of the 1:1·15 frequency ratio of the Front End's pass-band between the lower and upper ends of its tuning range, the pass-band of the audio signal presented to the Back End will vary by the same factor of 1:1·15. The function of the Back End is firstly to make the audio pass-band constant over the whole tuning range. It achieves this objective by allowing only 5 octaves of the audio spectrum to pass through to the audio amplifier and loudspeaker. The highest unattenuated frequency allowed through is thus 16 times the lowest unattenuated frequency allowed through. Each of the 5 permitted octaves is allowed to pass through its own one-octave wide tuned filter. This requires 5 different and separate one-octave filters wired in parallel, as shown in the diagram above.

Response trace of the 5 parallel acceptance filters of the Top to Ten TRF receiver. The centre frequencies chosen for the 5 parallel accep­tance filters are 110, 220, 440, 880 and 1760 Hertz. The trace on the left shows the 5 overlapping accep­tance bands peaked one octave apart. The horizontal axis shows frequency according to a logarithmic scale. The vertical axis shows the ampli­tude of the signal al­lowed through.

Composite response trace of the 5 parallel acceptance filters of the Top to Ten TRF receiver. The pass-band profile produced by combining the out­puts of the 5 acceptance filters is shown on the right. This now has the correct 5-octave bandwidth. How­ever, its sides are not yet sufficiently steep. In other words, the degree to which it rejects all frequencies above and below the desired pass-band is not yet ad­equate.

Response of the 2 band-bounding notch filters of the Top to Ten TRF receiver. For this reason, the signal, gained by merging the outputs of the 5 parallel acceptance filters, is amplified and then passed through two successive rejection (or notch) filters. Each of these strongly rejects signals at frequencies at – and close to – its tuning point (75Hz & 2kHz respectively), as shown in the trace on the left.

Composite response of all the audio filters in the Top to Ten TRF receiver. This causes a steep attenuation of the audio signal at the upper and lower boundaries of the desired five octave frequency range. The resulting pass-band now approximates much more closely to the ideal square all-or-nothing profile, as shown on the right. The output signal from the second notch filter is then passed on to a good quality audio amplifier.

The Acceptance Filters

I have decided to use 5 inductance-capacitance filters whose centre frequencies correspond to the A-note in each of 5 octaves of the piano. Middle-A on the piano has a frequency of 440 hertz. Each A-note going down the keyboard has half the frequency of the previous A-note. Each A-note going up the keyboard has double the frequency of the previous A-note. The centre frequencies for my 5 pass-band filters are therefore 110, 220, 440, 880, 1760 hertz.

Audio acceptance filter circuit used in the Top to Ten TRF receiver. A diagram of an LC (inductance-capacitance) pass-band filter is shown on the right. The inductive re­actance of the coil, XL=2πfL, where f is the frequ­ency of the presented signal and L is the value of its inductor in henries. The capacitive reactance of the capacitor, XC=1/(2πfC), where C is the value of the capacitor in farads. The filter passes the in­coming signal with least opposition when XC = XL.

The following calculator calculates the required inductance value in henries for a pass-band filter of a given centre-frequency and standard capacitor value. Type in your values for frequency and capacitance and press the carriage-return key within either of these fields. The required inductance appears in the third (bottom) field. The default values shown are for a filter which will allow through signals that fall within the octave centred on Middle-A [440 Hz].

Pass-band Frequency, Fmin Hertz
Chosen Capacitance, Cmax Farads
Required Inductance, L Henries

The table on the left shows the values thus calcul­ated for the 5 filters I need to limit my audio pass-band to frequencies which fall only within the 5 oct­aves I require. However, the calculations have given some awk­ward values for the inductances required. I would like to see how far the centre frequencies of my filters will be perturbed if I use the nearest stand­ard inductor values.

The following calculator takes the standard capacitor value from the previous cal­culator and calculates the filter's centre frequency from an entered inductor value. So, if I use a 130 millihenry inductor instead of the 130·8383053310797 millihenry inductor value given by the first calculator, I get a centre-frequency value of 441·4163908290642 hertz instead of 440 hertz. I can live with that.

Adjusted Inductance, L Henries
Centre Frequency, Fmin Hertz

0.00001000.200 113
0.00001000.050 225
0.00000100.130 441
0.00000100.030 919
The table on the right gives the centre-frequencies of my 5 filters where I am using more rounded values for the inductances. Of these, the worst is only about 4% out, which is somewhere in between the notes A and A#. I don't think that this could make any per­ceptible difference to the range of frequencies which will ultimately arrive at the list­ener's ears.

Star configuration of the pass-band filters in the Top to Ten TRF receiver. Each of the five pass-band filters must pass its respective octave of the audio signal. This necessitates that the 5 pass-band filters must operate in parallel. The output from the Back End's first op-amp must therefore be split 5 ways to provide a separate independent input for each filter. This splitting is done by what is, in effect, a 6-way star network of resistors, as shown on the left.

The 6 ways comprise one input and 5 outputs. The value, R, of each resistor must be one sixth the operating impedance of the op-amp and the filters. There must be a separate 5-way splitter for each of the two outputs from the balanced op-amp. Each pass-band filter thus comprises two identical instances of the following circuit.

Pass-band filter circuits used in the Top to Ten TRF receiver.

The values shown are for the 440 Hz filter. The four resistors, R, all have the same value in all filters, equal to one sixth of the impedance of the op-amp's outputs. The two resistors on the left are each part of a separate 6-way star splitter. The two resistors on the right are each part of a separate 6-way star signal merger, which merges the outputs of the 5 pass-band filters ready for input to the Back End's second op-amp. Ideally, I would include an op-amp in each filter, as show below.

Pass-band filter circuit including a 2-channel op-amp as used in the Top to Ten TRF receiver.

I would make the gain of the op-amp manually adjustable by means of a sliding variable resistor. This would allow me to even out any irregularity in the pass-band and also reduce the bandwidth in the presence of troublesome higher octave inter­ference.

Notch Filters

The upper and lower edges of the composite pass-band of the 5 filters so far de­scribed are not steep enough to completely avoid interference on frequencies just outside the pass-band. I shall therefore steepen these edges by placing notch rejec­tion filters, one either side of the pass-band, as shown in the following graph.

Response trace of the notch filters used in the Top to Ten TRF receiver.

All these signals should add up to a reasonably steep-sided rectangular pass-band.

Circuit of a generic notch filter used in the Top to Ten TRF receiver. A circuit diagram of the generic LC (inductance-capacitance) rejection (or notch) filter is shown on the right. The relationship between resonant fre­qu­ency, capacitance and inductance is the same as for an acceptance (or pass-band) filter. The same calculators, as before, can therefore be used also to calculate the values of the components (induc­tor and capacitor) required for the Back End's re­jection filters.

Recap: The coil's inductive reactance, XL = 2πfL, where f is the frequency of the presented signal and L is the coil's inductance in henries. The capacitor's capacitive reactance, XC = 1/(2πfC), where C is its capacitance in farads. The filter rejects the incoming signal with maximum opposition when XC = XL. The values shown in the above diagram are for a 75Hz rejection filter. This rejects (does not allow to pass through) signals with frequencies at and around 75 Hz.

The two rejection (notch) filter stages of the Back End are shown in the following diagram. These stages form a balanced two-channel system, using two-channel differential op-amps. One channel carries the positive half-cycles of the audio signal while the other channel carries the negative half-cycles of the audio signal. Since there are two stages with two channels, four notch filters are required, each shown in a red square. Thus there are two 75Hz filters and two 2kHz filters.

Schematic of the two-stage two-channel notch filter with op-amps as used in the Top to Ten TRF receiver.

I have used variable capacitors in the 2kHz notch filters. These variable capacitors are ganged. This allows me to move the notch frequency in case I need to eliminate a troublesome heterodyne on any particular frequency. The 0·1μF capacitance can be made up, in practice, of a lower value variable capacitor with an additional fixed capacitor.

The output from the second notch filter is passed - via a balanced feed - to a good quality audio amplifier and loudspeaker.

Useful References

©13 Sept to 05 Oct 2016 Robert John Morton