Note in the equivalent circuit of Fig. 45 that the capacitor...

Note in the equivalent circuit of Fig. 45 that the capacitor appears in parallel with the negative resistance. Determine the reactance of the capacitor at $1 \mathrm{MHz}$ and $100 \mathrm{MHz}$ if $C=5 \mathrm{pF}$, and determine the total impedance of the parallel combination (with $R=-152 \Omega$ ) at each frequency. Is the magnitude of the inductive reactance anything to be overly concerned about at either of these frequencies if $L_{S}=6 \mathrm{nH}$ ?

Key Concepts

Inductive Reactance

Inductive reactance characterizes the opposition that an inductor offers to changing currents within a circuit, calculated as Xl = ?L. At radio frequencies, even small inductances can produce significant reactance. Evaluating whether this reactance is of concern in a circuit requires comparing its magnitude to the other reactive elements present.

Parallel Combination of Impedances

This concept pertains to the method of combining two or more circuit impedances connected in parallel. The overall impedance is derived from the reciprocal of the sum of the reciprocals of the individual impedances. When combining reactive components (like capacitors) with resistive elements (including negative resistance), one must account for both magnitude and phase to obtain the correct total impedance.

Capacitor Reactance

This concept involves the opposition that a capacitor provides to alternating current, which is inversely proportional to both the frequency and the capacitance. It is commonly calculated using the formula Xc = 1/(?C), where ? is the angular frequency. This explains how at higher frequencies the reactance decreases, affecting the overall impedance seen in the circuit.

Negative Resistance

Negative resistance represents a circuit element whose voltage-current relationship yields power gain instead of the usual dissipation. In the context of the equivalent circuit, it is used to model active components that can counteract losses. Understanding negative resistance is crucial for analyzing circuits that exhibit oscillatory or amplifying behaviors.

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