Transformer or not transformer.
In the MW receiver we used a transformer to don't degrade the bandwidth of our antenna-tuner inserting the rest of the circuit. It's obvious that we have always a receiver antenna and we have to connect it to the receiver circuit so this is a general problem, therefore we understand that the transformer could resolve this problem in a very elegant way.
It' s important to observe that there is a price that we have to pay: first of all the high price for the materials (copper and ferrite) and second we lose in amplify factor (i repeat we preserve the bandwidth.)
We also see a "reverse" application of the transformer that is connecting a voltage source in series with a resistance at the secondary stage of a transormer, in the primary we have for example an high value of resistance, we find that we have "adapted the line" that is another very important and common problem building receiver in RF.
There is another clever solution to the problem of not degrade the Q factor of a resonant circuit: the use of two capacitance in a very particular way.
To study this solution we used two particular transformation that sound strange (but that are possible under certain frequency condition): the transformation parallel to series and the vice versa.
We have to understand that now we have the instrument to study complex circuits in an easy way, the observation is that we don' t use the articulated expression of the transfer function (with denominator not of the second grade).
Finally we see how to connect two different stage to obtain a wider passband filter (costant in a wide bandwidth) and further the concept of autotransformer that can simplify the realization of a transformer.
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