Single-tuned four-band crystal radio set using a two-value tank inductor

Summary: This article describes Version 'b' of a single-tuned four-band crystal radio set, sometimes called a "Benodyne" (constant bandwidth with maximum weak-signal sensitivity across the whole BC band). It is an attempt to achieve the following two objectives at a -3 dB RF bandwidth of about 6 kHz (relatively independent of signal strength), and constant, high efficiency across the entire AM broadcast band by using two values of inductance in the tank: 1) Best possible sensitivity on weak signals; 2) Loudest possible volume on strong signals. Version 'c' of this crystal radio set uses Litz wire, introduces a contra-wound coil and has a "narrow selectivity" setting. It may be viewed in Article #26.

Means are provided for increasing selectivity at a small sacrifice in sensitivity. This crystal radio set is not designed to have strong immunity to local pick-up from local "blowtorch" stations. Selectivity and insertion power loss figures from a computer simulation are given and compared with those of the actual physical crystal radio set. A way to tell if the detector is operating below, at or above its 'Linear-to-Square Law Crossover point' (LSLCP) is described. No external antenna tuner is necessary. An explanation of 'short wave ghost signals' and 'hash' is provided along with some suggestions on how to combat them. This version 'b' uses only one diode and audio transformer configuration, as compared to the two used in the original obsolete version (now called Version 'a'). Also a new way to make a higher Q, low inductance coil using all the wire and coil form of the high inductance coil is described. Finally, the small performance sacrifice at the high end of the band that occurs when more readily available and lower cost parts are used is discussed.

Additional benefits of the "Benodyne" type of tank circuit are: (1) Reduction of the the sharp drop in tank Q or sensitivity at the high frequency end of the BC band often experienced when only one value of tank inductance is used for the whole BC band. (2) Reduction of the tank Q from loss in the variable cap when using lower cost units that use phenolic insulation, such as the common 365 pF cap (see Figs. 2, 3, 4, and 5 in Article #24). The "two inductance value benodyne* circuit is used in the crystal radio sets in Articles #22 and #26. We assume here that the two "Benodyne" component inductors (see "The Tank Inductor" in Article #26) provide a tank inductance of 250 uH in the low frequency half of the BC band (520-943 kHz) and 62.5 uH in the high half (0.943-1.71 MHz). If the large 250 uH inductance setting were used all the way up to the top end of the BC band (as in the usual case), a total tuning capacity of 34.7 pF would be required at 1.71 MHz (Condition A). In the "Benodyne" circuit, with the 62.5 uH inductance setting used for the high frequency half of the BC band, a total tuning capacitance of 139 pF is required at 1.71 MHz (Condition B). Benefit (1) occurs because in condition A, a larger fraction of the total tuning capacitance comes from the typically low Q distributed capacity of the inductor than in condition B. This results in a higher Q total capacitance in condition B than in condition A. Benefit (2) occurs because The effective Q of a typical 365 pF variable cap, when used with a 250 uH tank, is about 500 at 1.71 MHz (see Fig. 3 in Article #24). The Q of the 365 pF variable cap, when set to 139 pF, is greater than 1500 (see Fig.5 in Article #24). This higher Q results in less loss and greater selectivity at the high end of the BC band in condition 2. A further benefit of the Benodyne circuit at the high end of the BC band is greater immunity from the Q reducing effects of surrounding high loss dielectric materials such as baseboard etc. The lossy stray capacity introduced is better swamped out by the high shunt tuning capacity used.

The design approach is to divide the AM band into several sub-bands in an attempt to keep the selectivity constant and the insertion power loss low. Many concepts described in various Articles on my Web Index Page, as well as some new ones, are used in the design.
The first step is to divide the band into two halves: Lo (520-943 kHz) and Hi (943-1710 kHz). Two-step shunt inductive tuning is employed to switch between bands. A tank inductance of 250 uH is used in the Lo band and of 62.5 in the high band.
The Lo band is further subdivided into two sub-ands: LoLo (520-700 kHz) and HiLo (700-943 kHz). The Hi band is also subdivided into two sub-ands: LoHi (943-1270 kHz) and HiHi (1270-1710 kHz).
Two different operational resistance levels at resonance, measured at the top of the tuned circuit (point 'A' in Fig. 5), are used at the center of the sub-bands. This impedance level is 125k ohms for the LoLo and LoHi bands and 250k for the HiLo and HiHi bands (excluding the resistive losses of the components used). These resistance values are made up of the parallel combination of the transformed RF antenna resistance and diode input RF resistance (at point A). These two resistances should be equal to each other to achieve a minimum insertion power loss, at the design bandwidth. This means that the transformed antenna and diode RF resistances are each 250k in the LoLo and LoHi bands and 500k in the HiLo and HiHi bands at point 'A'. The two different transformed RF antenna resistance values (at point 'A'), at the top of the tank are achieved by proper adjustment of a variable capacitor in series with the antenna (C7 in Fig. 5). The two different diode RF tank loading resistance values (at point 'A') are achieved by tapping the diode onto the tank at a point that is 70% of the turns up from ground for bands HiLo and HiHi. The tank is not tapped for the LoLo and LoHi bands, and connection is to the top of the tank.
The weak-signal audio output and RF input resistances of a diode detector are approximately the same and equal to 0.026*n/Is. The strong-signal audio output resistance of a diode detector approximately equals 2 times the RF resistance of its source. Compromise audio impedance transformation ratios are used to optimize performance on both weak and strong signals, thus maximizing sensitivity and volume.
The design is scalable. Less expensive parts that may have somewhat greater losses may be used with some penalty in sensitivity and selectivity at the at the high end of the band. See the Parts List for a listing of more easily available and lower cost parts than the ones used in the original de sign. A tradeoff between sensitivity and selectivity can be achieved by changing the ratio of C7 and C8. Less capacitance in C7 increases selectivity and reduces sensitivity, and vice versa.

To achieve a relatively constant -3 dB bandwidth of 6 to 8 kHz across the full range of 520 to 1710 kHz, with a relatively constant RF power loss in the RF tuned circuits of less than 4 dB.
To to provide adjustment capability for greater selectivity, or less RF loss when needed.
To provide optimal performance with external antenna-ground systems having a fairly wide range of impedance.
To provide a simple-to-use switching setup for comparison of a 'test' diode with a 'standard one'.
To provide a volume control that has a minimal possible effect on tuning, having a range of 45 dB in 15 dB steps. This was incorporated in the design because the two local 50 kW blowtorch stations ABC and WOR (about 10 miles away) deliver a very uncomfortably loud output from SP headphones from my attic antenna. A means of volume reduction was needed. This method of volume reduction actually increases selectivity by isolating antenna-ground resistance from the tank circuit.
Introduce a new (to me) method for constructing high Q low inductance value inductors.

The frequency response shape of the circuit shown in Fig. 2 is that of a simple single tuned circuit and can be thought of as representative of the nominal response of a single tuned crystal radio set. Consider these facts:

If Lt and Ct have no loss (infinite Q), zero insertion power loss occurs at resonance when Rs equals Rl. This is called the 'impedance matched' case. The power source (Vs, RS) sees a resistance value equal to itself (Rl). Also, the load (Rl), looking towards the input sees a resistance (RS), equal to itself. In the practical case there is a finite loss in Lt and CT This can be represented by an additional resistance Rt (not shown), shunted across the tuned circuit. The input resistance seen by (Vs, RS) is now the parallel combo of Rt and Rl and it is less than RS The impedance match seen by (Vs, RS) when the tank Q (Qt) was infinite is now destroyed. The impedance matched condition can be restored by placing an impedance transformation device between the source, (Vs, RS) and the tank. In the crystal radio set to be described, the Q of the highest Q practical inductor thought suitable for the design was found to be sufficient to enable about a 6 kHz loaded bandwidth to be obtained with about a 4 dB insertion power loss over the tuning range of 520-1710 kHz.
In Fig. 2, if tuning could be done with Lt alone, leaving CT fixed, the bandwidth would be constant. The problem here is that high Q variable inductors that can be varied over an approximately 11:1 range, as would be needed to tune from 520 to 1710 kHz do not exist. On the other hand, tuning by varying the value of CT by 11:1 will cover the range, but have two disadvantages. (1) Bandwidth will vary by 1:11 from 520 to 1740 kHz. (2) In the practical case, if the bandwidth is set to 6 kHz at the low end of the band, and an attempt is made to narrow the bandwidth at 1710 kHz by placing a capacitor in series with the antenna, the insertion power loss will become great.
The compromise used here is a coil design that can be switched between two inductance values differing by 4:1. The high inductance setting is used for the low half of the band and the low inductance setting for the high half. Capacitive tuning is used to tune across each band. The technique used here, in creating the two inductances, enables the Q of the low value inductance to to be much higher than would be the case if a single coil of the same diameter but with fewer turns was used. This technique uses two coils, closely coupled, and on the same axis. They are connected in series for the large inductance and in parallel for the small one. The small inductance has a value 1/4 that of the large one and about the same Q at 1 MHz. The innovation, so far as I know, is to use the full length of wire used in the high inductance coil, occupy the same cubic volume, but get 1/4 the inductance and keep the same Q as the high inductance co il.
The high and low bands are each further subdivided giving a total of four bands (LoLo, HiLo, LoHi and HiHi). If this was not done, we would be faced with a bandwidth variation of about 1:3.3 in each band. The bands are geometrically divided and are: 520-700 (LoLo), 700-943 (HiLo), 943-1270 (LoHi) and 1270-1710 (HiHi) kHz. The bandwidth should vary 1:1.8 across each sub-band. The same relation should hold between the HiHi and LoHi band. The bandwidth at the center of each of the four bands are made approximately equal to each other by raising the loading resistance of the antenna and diode on the tank by a factor of two in band HiLo compared to the value used in band LoLo. The same adjustment is used for bands HiHi and LoHi.

Fig. 3a shows the simplified Standard Dummy Antenna circuit, described in Terman's Radio Engineer's Handbook, for simulating a typical open-wire outdoor antenna-ground system in the AM band. R1=25 ohms, C1=200 pF and L1=20 uH. See Article #20 for info on how to measure the resistance and capacitance of an antenna-ground system. The values shown for Fig. 3a are used in the design of the crystal radio set. R1 represents primarily the ground system resistance. C1 represents the capacitance of the horizontal wire and lead-in to ground and L1 represents the series inductance of the antenna-ground system.

The values of R1, C1 and L1 in Fig. 3a will be considered to be independent of frequency. To the extent that they do vary with frequency, C7 and C8 in Fig. 5 can be adjusted to compensate. The current-source equivalent circuit of the antenna-ground circuit is shown in Fig. 3b. To a first degree of approximation, in the practical case, C2 in Fig. 3b is independent of frequency. R2 will vary approximately inversely with frequency. We will ignore the effect of L2, since its value is large, except when approaching the first resonance of the antenna-ground system. The design approach is to place a variable capacitor C3 in series with the antenna circuit (Fig. 3a) to enable impedance transformation of the antenna-ground circuit to an equivalent parallel RC (Fig. 3b), the R component of which can be adjusted by changing the value of the C3 to follow a desired relationship vs frequency. One of the objectives of the design is to enable as constant a bandwidth as possible vs. frequency. This requires the aforementioned equivalent parallel R2 component to vary proportionally with the square of the frequency if capacitive tuning is used as it is here, in each sub-band (Q must be proportional to frequency for a constant bandwidth). This design attempts to accomplish this in the center of each frequency band. Performance is close at band edges.

The topology of the single tuned circuit is changed from band to band as shown in Fig. 4 below.

The resonant RF resistance values at the top of C8 (Fig. 4), from the transformed antenna resistance, (at the center of each sub-band) are designed to be: 250k ohms for bands LoLo and LoHi, and 500k ohms for bands HiLo and HiHi. Since the diode is tapped at the 0.7 voltage point for bands HiLo and HiHi, it sees a source resistance at resonance of: 125k for bands LoLo and LoHi and of 250k ohms for bands HiLo and HiHi. These figures apply for the theoretical case of zero loss in the tuned circuits (infinite Q). In a shunt capacitively tuned crystal radio set, loaded with a constant resistive load, the bandwidth will vary as the square of the frequency. To understand why, consider this: When the resonant frequency of a tuned circuit loaded by fixed parallel resistance is increased (from reducing the total circuit tuning capacitance), the shunt reactance rises proportionally, giving rise to a proportionally lower circuit Q. But, a proportionally higher Q is needed if the bandwidth is to be kept constant. There for, the square relation.

In the practical case, we are faced with two problems. (1) How should we deal with the fact we work with finite Q components? (2) At high signal levels (above the LSLCP), the RF load presented by the diode to the tuned circuit is about 1/2 the audio load resistance, and at low signal levels (below the LSLCP) the RF load presented to the diode is about 0.026*n/Is ohms. Compromises are called for.

Parts List - All components are chosen for the best possible sensitivity at a -3 dB RF bandwidth of 6 kHz (except for not using litz wire in the inductor).

** For lower cost, the following component substitutions may be made: Together they cause a small reduction in performance at the high end of the band (about 1.75 dB greater insertion power loss and 1.5 kHz greater -3 dB bandwidth). The performance reduction is less at lower frequencies.

Mini air-variable 365 pF caps sold by many distributors such as The Crystal Set Society and Antique Electronic Supply may be used in place of the ones specified for C7 and C8.
18 ga. (0.040" diameter) "bell wire" supplied by many distributors such as Home Depot, Lowe's and Sears may be used in place of the teflon insulated wire specified. This vinyl insulated bare copper wire is sold in New Jersey in double or triple twisted strand form for 8 and 10 cents per foot, respectively. The cost comes out as low as 3 1/3 cents per foot for one strand. The main catch is that one has to untangle and straighten the wires before using them. I have used only the white colored wire but I suppose the colored strands will work the same (re dielectric loss). The measured outside diameter of the wire from various dealers varied from 0.065 to 0.079". The high dielectric loss factor of the vinyl, compared to the teflon specified above will cause some reduction of sensitivity and selectivity, more at the high end of the band than the low end. I don't think the difference would be noticeable to a listener.
Radio Shack mini DPDT switches from the 275-327B assortment or standard sized Switchcraft 46206LR switches work fine in place of the specified Switchcraft 56206L1 and cost much less. See Article #24 for comparison with other switches. Any switch with over 4 Megohms Rp shown in Part 2 of Article #24 should work well as far as loss is concerned. Overall, losses in the switches have only a very small effect on overall performance.

The coil should be mounted with its axis at a 30 degree angle to the front panel as shown in Fig.1. The center of the coil form is 2 7/8" back from the rear edge of the baseboard and 5 5/8" to the left of its right edge. These dimensions are important, as is the actual size of the breadboard, if one wishes to construct a double-tuned four band crystal radio set out of two Version 'b' single-tuned four band crystal radio sets as described in Article #23.

**Table 1 - Switch Functions for Version 'b':**
SW1	15 dB volume control "capacitive" attenuator. 'Down' places a 15 dB loss in the input.
SW2	30 dB volume control "capacitive" attenuator. "Down' places a 30 dB loss in the input.
SW3:	'Up' position for operation in the LoLo (520-700) and HiLo (700-943 kHz) band. 'Down' position for operation in the LoHi (943-1270) and HiHi (1270-1710 kHz) band.
SW4:	Same as SW3.
SW5:	'Up' position for operation in the LoLo and LoHi band. 'Down' position for operation in the HiLo and HiHi band.
SW6:	'Up' position for normal crystal radio set operation, using a diode having an Is of about 100 nA. 'Down' position for increased selectivity, using a diode having an Is of about 15 nA in the #2 position, or for comparison testing of diodes.
SW7:	'Down' position for normal operation. 'Up' position to bypass the onboard audio transformers, if one wishes to use an external one.

The diode: This design is optimized for use with a diode having an n of 1.03 and a Saturation Current (Is) of about 82 nA, although this is not critical and other diodes can be used with good results. See Articles #0, #4 and #16 for info on n and saturation current (Is) of diodes, and how to measure them. If desired, and one has a favorite diode, its effective (Is) can be changed by applying a DC bias voltage, using perhaps, the 'Diode Bias Box' described in Article #9.

One suitable diode, the published parameters of which show an (Is) of 100 nA is a Schottky diode, the Agilent HBAT-5400. It is a surface-mount unit that was originally designed for transient suppression purposes. Measurements of many HBAT-5400 diodes seems to show that there are two varieties. One type measures approximately: n=1.03 and (Is)=80 nA. The other type seems to have an n of about 1.16 and an (Is) of about 150 nA. Both work well but the former works the best. This part, available in an SOT-23 package is easily connected into a circuit when soldered onto a "Surfboard" such as manufactured by Capital Advanced Technologies (http://www.capitaladvanced.com/), distributed by Alltronics, Digi-Key and others. Surfboard #6103 is suitable. The HBAT-5400 is also available in the tiny SO-323 package that can be soldered to a 330003 Surfboard.

The Agilent HSMS-2860 microwave diode (Specified Is=50 nA) is available as a single or triple with three independent diodes in the SO-323 and SO-363 packages, respectively. The Agilent number for the triple diode is HSMS-286L. I find it to be particularly good for DX in this crystal radio set. It is a convenient part since one can connect it using only one section (shorting the unused ones) or with two or three in parallel. This gives one a choice of nominal saturation currents of 50, 100 or 150 nA. Samples of this part I have tested measured about 35 nA per diode, not 50. I don't know the normal production variations. The only disadvantage of this diode, as far as I know, is its low reverse breakdown voltage which may cause distortion and low volume on very loud stations. It has the advantage, as do most Schottkys, of having much less excess reverse leakage current than do germanium diodes. This helps with volume and selectivity on very weak stations.

Infineon makes a BAT62 Schottky diode in several different quite small surface mount packages. The single BAT62 is physically the largest. It has a specified (Is) of about 100 nA and performs quite well. Be forewarned that the diode parasitic series resistance is a high 100 ohms in this diode. A resistance even this high should not have a noticeable effect on the performance of a crystal radio set.

Most germanium diodes have too high a saturation current for the best selectivity and should to be back-biased or cooled for optimum performance. See Article #17A for more info on this. Different type diodes may be connected to the terminals labeled Diode #1 and Diode #2, with either one selectable with SW6. When one diode is selected, the other is shorted. This feature makes it easy to compare the performance of a 'test' diode with one's 'favorite' diode. Another use is to place one's best DX diode in one position and one having a very low reverse leakage resistance at high reverse voltages in the other. This will maximize strong signal volume and minimize audio distortion.

A good choice for this crystal radio set is a diode having a relatively low saturation current such as 3 or 4 Agilent HSMS-2820 or HSMS-2860 diodes in parallel as Diode #1 for high selectivity and sensitivity on weak signals, and an Agilent HBAT-5400 or one of the lower saturation current germaniums as Diode #2 for low distortion and maximum volume on strong stations. Don't use two diodes in series if you want the best weak signal sensitivity in any crystal radio set. The result of using two identical diodes in series is the simulation of an equivalent single diode having the same (Is) but an n of twice that of either one. This reduces weak signal sensitivity.

The inductor for this single tuned crystal radio set is made up of the four closely coupled inductors L1, L2, L3 and L4. The inductance from point A to ground (Fig. 5) is 250 uH when SW3 is in the 'up' position (used for low band reception) and 62.5 uH in the 'down' position (used for high band reception). Better performance from a higher tank Q at the high frequency end of band B may be obtained by using the "contra-wound" coil winding technique described in Article #26. This minimizes distributed coil capacitance in band B as opposed to the winding connections used here that minimize coil distributed capacity in band A.

Audio impedance transformation from the audio output resistance of the diode detector to 'series connected' 1.2k ohm sound-powered phones is provided by the audio transformers. If one wishes to use 300 ohm sound-powered phones with two 600 ohm elements connected in parallel instead of series, a very good low loss transformer choice is the 100k-100 ohm transformer from Fair Radio Sales, #T3/AM20. The configuration of two Calrad transformers shown on line 2 of the Calrad chart in Article #5 is also a good choice. C11, along with the shunt inductance of the transformer and the inductance of the sound powered phones form a high-pass filter, hopefully flat down to to 300 Hz. R3 is used to adjust the DC resistance of the diode load to the AC impedance of the transformed effective AC headphone impedance. C10 is an audio bypass.

The two variable capacitors C7 and C8 interact substantially when tuning a station. C7 mainly controls the selectivity and C8 mainly controls the resonant frequency. If the antenna-ground system being used has a resistance larger than 25 ohms, C7 will have to be set to a smaller capacitance in order to maintain the proper resonant resistance at point A in Fig. 5. If the capacitance of the antenna-ground system is greater than 200 pF, C7 will also have to be set to a lower value than if it were 200 pF.

The "capacitive" attenuators controlled by SW1 and SW2, used for volume and selectivity control, are designed so as to cause minimal tank circuit detuning when the equivalent circuit of the antenna-ground system used has the same values as the old IRE simplified Dummy Antenna recommended for testing Broadcast Band radio receivers. It consisted of a series combination of a 200 pF cap, 20 uH inductor and a 25 ohm resistance. The geometric mean of the sum of the reactances of the capacitor and inductor at 520 and 1710 kHz is (-605) ohms. This is the reactance of a 279 pF capacitor (characteristic capacitance of the "capacitive" attenuator) at 943 kHz, the geometric mean of the BC band of 520-1710 kHz. The "capacitive" attenuators were designed for the specified attenuation values (15 and 30 dB) utilizing the 500 ohm resistive pi attenuator component values table shown in the book "Reference Data for Radio Engineers". The resistor values for 15 and 30 dB "capacitive" attenuators were normalized to 605 ohms, then the "capacitive" attenuator capacitor values were calculated to have a reactance, at 943 kHz, equal to the value of the corresponding "capacitive" attenuator shunt or series resistance. Since the "capacitive" attenuators, when switched into the circuit, isolate the antenna-ground system resistance from the tank circuit, selectivity is increased. This is a convenient feature, since less retuning is required than if selectivity is increased by reducing C7 and increasing C8. If the series capacitance of the equivalent circuit of one's own antenna-ground system is 200 pF, at 943 kHz, practically no retuning is required.

If the equivalent L and C of one's own antenna-ground system differ substantially from those of the simplified IRE dummy antenna used here, one can normalize the values of the capacitors used in the "capacitive" attenuators to match ones's own antenna-ground system. A method for measuring the parameters of one's own antenna-ground system is shown in Article #20.

4. 'Loop Effect' of the tank inductor, and how it can be used to tame
local 'Blowtorch' stations when searching for DX.

One can use local signal pickup by the tank (loop effect) to reduce the effect of interference from strong stations by rotating the crystal radio set about a vertical axis. The correct angle will generally reduce it.

Note: When altering selectivity by changing switch positions, always re-balance the relative settings of C7 and C8.

6. Just how loud is a station that delivers the amount of power necessary to operate the Diode Detector at its 'Crossover Point' between Linear and Square-Law Operation?

Many Articles in this series have talked about the 'Linear-to-Square-Law Crossover Point' (LSLCP). Please bear in mind that the LSLCP point is a point on a graph of output DC power vs input RF power of a diode detector system. It is not a point on a graph of DC current vs voltage of a diode. Two things can be said about a detector when it is fed a signal that operates it at its LSLCP. (1) A moderate increase of signal power will move the detector into its region of substantially linear operation. (2) A similar moderate decrease of input power will move it closer to its region of substantially square law operation, where a 1 dB decrease of input power results with a 2 dB decrease of output power. For more info on the LSLCP, see Article #15A.

The crystal radio set described in this Article is operating at its LSLCP if the rectified DC voltage at the 'Diode Bias' terminals is 53 mV, a diode having a Saturation Current (Is) of 82 nA and an ideality factor (n) of 1.03 is used (such as a selected Agilent HBAT-5400), and if R3 is set to 325k ohms. At this point the diode rectified current equals two times its Saturation Current. The volume obtained is usually a low to medium, easy-to-listen-to level.

All single tuned crystal radio sets may be, in fact, considered double tuned (except single tuned loop receivers). The second response peak arises from resonance between the equivalent inductance of the antenna-ground system and the impedance it sees, in this case, the series combination of capacitors C7 and C8. This peak usually appears at a frequency above the broadcast band and gives rise to the possibility of strong so-called 'short wave ghost' signal interference when a short wave station has a frequency near the peak . The response at this ghost frequency can be made somewhat weaker and moved to a higher frequency if the antenna-ground system inductance is reduced. One can use multiple spaced conductors for the ground lead to reduce its inductance. I use a length of TV 300 ohm twin lead, the two wires connected in parallel for this purpose. Large gauge antenna wire, or spaced, paralleled multiple strands helps to reduce the antenna inductance (flat top antenna). If the down-lead is long compared to the ground lead, use multiple, paralleled, spaced conductors to reduce its inductance (similar to using a 'cage' conductor).

Another possible cause of 'ghost' signal reception resides in the fact that the response of the so-called single tuned circuit does not continuously drop above resonance as frequency rises, but only drops to a relatively flat valley before rising again to the second peak. The frequency response above the main (lower) peak would drop monotonically (true single tuned operation) if the second peak did not exist. The relatively flat response valley that exists between the two peaks, provides the possibility (probably likelihood) of interference 'hash' if several strong stations are on the air at frequencies in the valley range. It also is the cause of a strong local station, above the frequency of a desired station "riding through" and appearing relatively constant even if the tuning dial is moved. The response should drop at a 12 dB per octave rate above the second peak. A useful side effect of the response behavior of this type of circuit is that the response below the main resonance drops off at an extra fast rate of 12 dB per octave rate instead of an expected 6 dB.

The most effective way to substantially eliminate 'short wave ghost' and hash reception is to go to a double-tuned circuit configuration or to use traps.

Spurious FM reception caused by so-called FM 'slope' detection can occur from close by local FM stations if a spurious FM resonance appears somewhere in the circuitry of a crystal radio set. If ground wiring is not done properly in the crystal radio set, spurious signals can get into the detector. The thing to do here is to run all the RF and audio grounds to one point as shown in Fig.5. Sometimes a small disc bypass capacitor, 22 pF or so, placed across the diode will help.

Another way to try to reduce FM interference is to put a wound ferrite bead 'choke' in series with the antenna and/or ground leads. In order not to affect normal BC band reception, the resultant ferrite inductor should have a reasonable Q and a low inductance in the BC band. It should also exhibit a high series resistance at FM frequencies. Suitable wound ferrite chokes (bead on a lead) are made by the Fair-Rite Corp. as well as others. Two types available from Mouser are #623-29441666671 and #623-2961666671. This suggestion may also help reduce "short wave ghost" signal reception.

Fig. 7 shows the simulated frequency response at the center of the LoLo band, from the antenna source to the RF input of the diode. The red graph and figures in the left panel show an insertion power loss of 2.4 dB with a -3 dB bandwidth of 6 kHz, along with the spurious response peak at 4.4 MHz, caused by the antenna-ground system inductance. The insertion loss at the spurious peak is 15 dB. The loss in the valley is 40 dB. The right graph and figures show the Input Return Loss (impedance match) at resonance to be -12.2 dB. The output return loss (not shown) is the same.

Fig. 8 shows the simulated frequency response at the center of the HiHi band, from the antenna source to the RF input of the diode. The red graph and figures in the left panel show an insertion power loss of 4.1 dB with a -3 dB bandwidth of 6 kHz, along with the spurious response peak at 6.9 MHz, caused by the antenna-ground system inductance. The insertion loss at the spurious peak is 20 dB. The loss in the valley is 47 dB. The right graph and figures show the Input Return Loss (impedance match) at resonance to be -8.5 dB. The output return loss is the same.

Every effort should be made to achieve as high an unloaded tank Q as possible, in order to minimize RF loss at the desired -3 dB bandwidth (selectivity), and especially when using narrower bandwidths. Somewhat greater insertion power loss and/or broader selectivity may result if components having a greater dielectric loss than those specified are used. Sensitive areas for loss are:

Q of the coil. See Table 2 for the Q values realized in the tank circuit.
Stator insulation in the variable caps C7, C8.
Skin-effect resistive loss in the variable capacitor plates. Silver plated capacitor plates have the least loss, brass or cadmium plated plates cause more loss. Aluminum plates are in-between. Rotor contact resistance can be a problem.
Contact support plastic used in slide switches SW3, 4, 5 and 6.
Front panel material.
Coil form material. Styrene has 1/10 the dielectric loss of PVC. High impact styrene forms are available from Genova Products at their retail store: http://genovaproducts.com/factory.htm . These forms are listed as drain couplers.
Capacitive coupling from any hot RF point, through the wood base to ground must be minimized because it tends to be lossy and will reduce performance at the high end of band A and band B. The steps I took to reduce these losses are: (1) Mounting C7 to the baseboard using strips of 0.10" thick, 0.5" wide and 1.5" long high-impact styrene as insulators and aluminum angle brackets screwed to the baseboard and (2) and connecting these brackets to ground. This isolates the lossy dielectric of the baseboard from the hot end of C7. See Fig. 1. Ceramic stand-off insulators can be adapted, in place of the styrene strips for the job. Another way to mount C7 is to make a mounting plate from a sheet of low loss dielectric material, somewhat larger than C7's footprint, and screw C7 on top of it. Holes made in the plate can then be used, along with small brackets or standoffs to mount the assembly onto the baseboard. Don't forget to wire the metal mounting pieces to ground. These same considerations apply to any metal coil mounting bracket, close to a hot end of the coil, used to mount the coil form to the baseboard. The bracket should be grounded.
The physical size of the coil is important. A large size coil was chosen to enable a high Q. Medhurst's work enables one to calculate the Q of a solenoid wound with solid copper wire, provided that: 0.4<do/t<0.8. do=diameter of the wire, t=center-to-center spacing of the turns. If this relation is followed, for a given physical volume, the maximum Q will occur when D=L, where D=diameter of the coil and L=length of the coil. The Q is then proportional to D(=L). Much care is required in measuring the Q of physically large high Q coils. The method I favor is given in Part 9, above.

In use, C7 and C8 are usually set to different values to achieve the design-bandwidth of 6-7 kHz. However, if they are set to the same values, a frequency calibration chart can be made for each band as shown above. The bold figures indicate the approximate position of each band when the crystal radio set is driven by the standard antenna-ground system. There is sufficient extra capacitance range available in C7 and C8 to handle antenna-ground systems that differ substantially in impedance from the standard dummy antenna used in the design.

The data in Table 4 shows the insertion power loss in the crystal radio set when driven by an RF signal that is amplitude modulated at 50% by a 400 Hz sine wave. See Article #11 on how to measure the insertion power loss and bandwidth of a crystal radio set. The audio output power was set to -70 dBW for each reading. The available carrier input power supplied to the crystal radio set was about -60 dBW, with a total available sideband power of about -66 dBW. The audio output power is that delivered by the diode detector to the audio load and does not include losses in an audio transformer. One should add about 1.0-1.5 dB to the insertion power loss shown in Table #4 to allow for audio transformer loss. The reason the audio transformer loss does not show up in the measurements is that the audio transformers (T1 and T2) were not used. SW7 was placed in the UP position, providing a direct high impedance output from the diode detector. The Zero Loss Unilateral 'Ideal Transformer' Simulator described in Article #14 was used to provide a 320k to 1200 ohm impedance transformation, close to that provided by T1 and T2 in actual crystal radio set operation.

Note: The diode rectified DC voltage at the power levels used above is 0.51 volts. At this power level, a SPICE simulation of the detector shows a theoretical diode detector insertion power loss of 1.4 dB.