Basic Circuit Theory
Answers to RF Cafe Quiz #19

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RF Cafe: Kirchhoff's Current Law diagram from Wikipedia website1. Which circuit law states that the sum of all currents into and out of a node equals zero?

c) Kirchhoff's Current Law.

This diagram illustrates the principle.

2. How much power is dissipated by an ideal 100 pF capacitor fed by a 1 Vpk-pk sinewave at 10 MHz? Hint: Z = 1/(2πfC)

d) 0 W.

An ideal capacitor or inductor dissipates no power, since power is a function of the real part of a complex impedance (R ± jX). Ideal capacitors and inductors store and release energy without consuming it (by releasing heat).

3. What causes a ground current loop?

c) More than one ground potential in a circuit.

A ground current loop occurs when "ground," or the supposed 0 V point, exists at more than one potential in a common circuit. The difference of potential causes a current to flow, often creating a noise component.

4. What type of filter does this circuit represent?

c) Bandpass.

An ideal series tank circuit passes energy at its resonant frequency with zero impedance (short circuit), and a parallel resonant circuit presents infinite impedance (open circuit). So, if both are tuned to the same frequency (although usually there is an offset), then at resonance the circuit appears as a short between the upper terminals and an open circuit wrt the lower terminals.

5. How many poles does the filter in Q4 have?

c) 2 poles.

Each resonant LC tank generates a pole in the transfer function.

Operational Amplifier OpAmp Integrating6. What is the configuration of the opamp shown here?

a) Integrator.

The transfer function is

RF Cafe: Transformer7. What is the secondary voltage of this transformer?

d) 2 V.

The secondary:primary turns ratio is 20:100, or 1:5. Voltage ratio is proportional to the turns ratio, so the secondary voltage is 10/5 = 2V

8. What is the impedance of the transformer secondary in Q7?

d) 4 Ω.

The impedance ratio is proportional to the square of the turns ratio, so the secondary impedance 100/52 = 4 Ω.

9. In an ideal system, what is the minimum sampling rate to prevent aliasing of a signal with a maximum frequency of 100 kHz?

b) 200 kHz.

The Nyquist Sampling Theorem demonstrates that a band-limited signal must be sampled at a rate at least twice the highest frequency in the original signal in order to prevent aliased content in the reconstructed signal. Here is a nice little applet that illustrates the sampling principle. Set the original signal for 150 Hz, and the sample rate to 300 Hz (2x the original) to see that the reconstructed signal is an exact duplicate of the original. Ditto for 350 Hz. Now, set the sample rate to 200 Hz or 100 Hz and note the added frequency components in the reconstructed signal.

10. Which type of diode typically has the lowest forward bias voltage for a given current?

d) Schottky.

A Schottky diode is very similar to a standard P-N junction diode, except instead of using an implanted p-layer, the rectification occurs at the interface between a barrier metal and the silicon layer. Here are typical I-V charts for the four types of diodes (compare at 25°C)


RF Cafe: GaAs diode I-V curve (TI TIL156)     RF Cafe: Germanium diode I-V (Microsemi 1N34A)

  GaAs Diode                                                       Germanium Diode


RF Cafe: Silicon diode I-V curve (Fairchild 1N4148WS)    RF Cafe: Schottky diode I-V curve (Fairchild RB521S30)

                Silicon Diode                                                            Schottky Diode