High frequency Models of Transformer, Inductor and Capacitor

The most used couplings in the oscillation circuits and selective amplifiers are the transformer coupling, inductive or capacitive divider. For high frequency analysis of the circuits it's very important to take care of circuit components characteristics at those frequencies. Therefore, it should be applied modeling of the components of the circuit proper to the working band of frequencies. There are several physical appearances like skin effect, whirlwind currents, magnetic field spreading or material aging, which significantly affect the quality of the inductive component and they leads to more complex models of transformer and inductor coil. From the other hand, the loss in the dielectric material and the resistance of the connections of the capacitive component leads to more complex modeling of the real capacitors. The apply of the h-parameters model of the transistor is not proper at frequencies above 1 MHz because of its frequency dependence. In that cases more appropriate is using of the Pi-hybrid model of the transistor, or using of the Y-parameters for the transistor modeling at frequencies from 10 to 50 MHz. A special problem is the isolation of the signal processing circuits from the power supply for which in most cases are used RFC (radio-frequency) filters, then decoupling of the stages of the amplifier or reducing of the effects from the scattered (stray) capacitances, and so on. The transformer model is shown on Picture 1, on Picture 2 is shown the inductor model and on Picture 3 is shown the capacitor model.

Picture 1: Transformer model

Picture 2: Inductor model

Picture 3: Capacitor model


As a result of the interaction which the output is doing to the input circuit or trough the parasitic connections in the circuit or through the active elements (Miller's effect), under certain conditions the selective amplifier circuit can start self-oscillating. But, even when there is no self-oscillating, the feedback connections can have an inconvenient affect on the selective characteristic and on the response of the amplifier, too. For that reason, it's necessarily to neutralize the impact of the inner feedback connections in order to achieve stable working state of the amplifier. The neutralization is usually done with the external feedback connection taken from the output and added to the input of the circuit with proper amplitude and phase which will compensate the effects of the internal coupling. The circuit configuration of the selective amplifier that we discussed before actually was self-oscillating, as we can see from its output voltage plot.