Electronic – Having a series instead of parallel LC circuit in a crystal radio

The first circuit in your question only exists in badly designed homework problems.

The reason is that an ideal capacitor in parallel with an ideal voltage source does nothing. The ideal voltage source can supply whatever current is needed to drive the capacitor to it's level without sagging, so the capacitor provides no filtering.

but...

In the real world there are no ideal voltage sources. They have series resistance. Or if they're located far from the point of load, there's a series inductance between the source and the load. This is the scenario where a parallel capacitor is useful.

Combined with the voltage source's parasitic resistance, the parallel capacitor provides filtering and reduces noise at the load.

Also, for more complex loads than the simple resistor in your circuit, if the load current varies (for example if it's a digital logic chip with it's outputs changing state), the parallel capacitor can provide the necessary current, which the voltage source may not be able to do because of its parasitic resistance or inductance.

okay, so do you need a resistor in series with your capacitor?

Generally no.

But there are instances where it is used.

One is, when you have a very large capacitor value and you need to limit the inrush current when the voltage source is turned on. In this case you often use a negative-tempco (NTC) resistor to limit resistance during the initial turn-on, but have low loss once it is heated up by current through it.

Another case is that sometimes an RC can be more effective at suppressing noise than a simple capacitor, because the capacitor itself cannot take energy out of the circuit --- it can only store it for later. The series resistor can actually dissipate energy from the circuit.

There are three advantages to driving the resonant L-C tank via tranformer coupling than directly from the antenna:

1. It changes the impedance. The impedance of the signal coming from the antenna is probably in the 50-300 Ω range. Crystal radios are usually listened to with high impedance headphones, usually around 2 kΩ. Having a 100 Ω source driving a 2 kΩ load is inefficient, which ultimately means lower volume.

2. The detector diode drop is a smaller fraction of the output voltage. The transformer steps up the voltage, making it higher than what comes out of the antenna directly. The forward drop of the dector diode is fixed, so it is less relative to the signal after that signal has been increased in voltage by the transformer. This means lower strength radio stations will still produce some output, and the output you get will have less distortion.

3. Better selectivity. The relatively low impedance of the antenna dampens the resonance of the L-C tank circuit. Another way to say this is that it lowers the Q of the resonant circuit. This means its resonant peak is more spread out, which means that the radio can't be tuned as well to a single station. The effect is that strong stations will appear to spill over into nearby frequencies.