Transmitter + Receiving Antenna + Selective Crystal Set or Radio Receiver

PRIMARY ,-----¦¦-----,             ,------------,     SECONDARY
CIRCUIT ¦     C1     ¦   Coil      ¦            ¦      CIRCUIT
        ¦            ¦   Coupling  ¦            ¦
        O         L1 $   Coeff.    $ L2        === C2
 Input               $             $            ¦
 From                $             $ Coil tap   ¦
 Antenna             $  Mutual     $<----------------¦<-----,------O
        O            $  Inductance $ for load   ¦   Diode   ¦   Hi-Z
        ¦            ¦  Between    ¦            ¦          === Phones
        ¦  Coil loss ¦  Two coils  ¦ Coil loss  ¦    2000pF ¦
        '----####----'             '----####----'-----------'------O

This "crystal" receiver uses two loosely-coupled tuned circuits. The circuit may also be used as a preselector in front of an untuned receiver. The load can be matched to L2 and C2 by changing the coil tap. The antenna can be matched to the tuned circuits by varying the coupling coefficient between the two coils and by varying C1 or L1. Another application is a balanced-to-unbalanced antenna tuner.

How to Use the Examples For calculated examples hit keys 'O' or 'P'.
First change test frequency to the resonant frequency of secondary circuit. The secondary circuit is the most selective and is tuned to the wanted signal. Perform the following operations while observing load volts and load power: Vary C1 or L1 such that primary input reactance is equal and opposite in sign to the input reactance of the antenna. Volts across load and load power have now been maximized. Now vary coupling coefficient to maximize load volts again. Critical coupling is that at which maximum power is transferred from primary to secondary circuit. These operations may interact with each other. So repeat. Bandwidth and radiation ohms may be inaccurate when antenna length > lambda/3. Optimum setting of the coil tap point is done automatically by the program, so there is no change in load power when the value of load resistance is changed.

Miscellaneous Notes and Assumptions
The transmitting antenna is an LF/MF broadcasting, omni-directional vertical. Receiving antenna is an inverted-L, height = 1/3rd length, fed against ground. The groundwave path is described in terms of soil resistivity in ohm-metres. An ohm-metre is the soil resistance between opposite faces of a 1-metre cube. For hi-Z phones, in the absence of accurate data, enter load R = 1000 ohms. Efficiency = Load Power/Total power collected by the antenna. Q*XL2 = unloaded impedance of secondary circuit L2 and C2 in parallel. Check all input data is as intended before using results. Easy to make errors. Tap fraction is fraction of turns on coil L2 to obtain a match with the load.

Computed tapping point is an optimum value. To increase it reduces selectivity. Tuning capacitor Q's are assumed to be 20 times the entered value for coil Q. The working value of the primary circuit Q is much reduced by antenna damping. 3dB bandwidth occurs at the half-power points or 0.7071 signal voltage points. All computed signal voltage levels are in milli-volts. Power is in micro-watts. Computed antenna data is accurate only at or near the test frequency setting. The test frequency is usually set to the secondary circuit resonant frequency. So remember to change the test frequency whenever L2 or C2 are changed. But remember when changing test frequency computed antenna data also changes.

Most of the receiver's working selectivity is due to the secondary circuit. Vary test frequency only to obtain the 3dB bandwidth of the frequency response. After entering a complete set of data, remember to first set frequency. Then vary L1 or C1 for primary circuit input reactance to be equal and of opposite sign to antenna input reactance to maximize load volts and/or load power. Then vary coupling coefficient for a greater maximum signal level. When constructing a receiver avoid over-coupling as it degrades selectivity. Over-coupling results in a sloping double-hump in the frequency response. There is a negligible gain in receiver sensitivity to be obtained by over-coupling. To improve the number of digits in computed data, change Tx power or path kM. The circuit may be simplified by putting C1=10 uF. C1 is then a short circuit. So when the antenna is less than 1/4-wavelength long and its input reactance is negative the primary circuit can be resonated with L1 alone.

A Tuning Procedure to Obtain Optimum Results (There are others)

• The antenna will usually be less than 1/4-wave long. Length < 75/F MHz metres.
• Select practical values of L2 & C2 to resonate at the desired signal frequency.
• Set L1 = L2 and C1 = C2 to obtain practical starting values over a frequency range.
• Important - Set test frequency to be exactly equal to desired signal frequency.
• Initially set coil coupling coefficient to a small value, about 1/2Q or 1/3Q.
• Set transmit power and path kM for a 2 or 3 digit, readable load power level.
• Vary C1 for a maximum computed load power level and leave C1 there.
• Vary coupling coefficient for a greater maximum power level and leave it there.
• Slowly vary test frequency on either side of signal frequency:
  - to find HIGHER test frequency at which load power falls to HALF of previous maximum.
  - to find LOWER test frequency at which load power falls to HALF of previous maximum.
• Subtract lower value of test frequency from higher value to find 3dB bandwidth.

Further Notes
It will be found that adjusting L1 or C1 for max power in the load resistance corresponds to adjusting L1 or C1 to make the primary input reactance equal to the antenna input reactance but of opposite sign. It is a partial conjugate match.

It will also be found when this is done, followed by a 2nd adjustment of the coupling coefficient for maximum load power, the power efficiency is near to 25 percent. This is not surprising because half the power is lost in the impedance match and another half of the power is lost in matching the load to the secondary circuit impedance via the tapped secondary circuit coil. Efficiency is defined as power in the load divided by power collected by the antenna.

Although initial values of C1 and C2 can be identical it is not possible for primary and secondary circuits to track each other over a band of frequencies. This is because antenna reactance, itself a complicated function of frequency, is confused with the reactances of L1 and C1.

But note, if C1 and C2 are ganged together, over the range of C1 and C2 there is one setting at which both primary and secondary circuits are tuned to the same signal frequency. A 3rd variable trimming capacitor is needed for perfection but this applies to all ganged tuning circuits involving an antenna.

Run this Program from the Web or Download and Run it from Your Computer
This program is self-contained and ready to use. It does not require installation. Click this link Xtl_Set then click Open to run from the web or Save to save the program to your hard drive. If you save it to your hard drive, double-click the file name from Windows Explorer (Right-click Start then left-click Explore to start Windows Explorer) and it will run.