Conquer Radio Frequency
Answers to RF Cafe Quiz #55

Return to RF Cafe Quiz #55

This quiz is based on the information presented in Conquer Radio Frequency, by Francesco Fornetti.

This material, which includes a full-color textbook and over 12 hours of video tutorials (in mp4 format on enclosed DVD-R), provides a comprehensive guide for the RF and Microwave engineering student or junior professional. It allows the reader to achieve a good understanding of the foundation theory and concepts behind high frequency circuits as well illustrating the most common design and simulation techniques for passive and active RF circuits. A preview of the textbook, a comprehensive description of the content of the video tutorials and sample video tutorials are available on the Explore RF website - http://explorerf.com/conquer-radio-frequency.html

Note: Dr. Fornetti personally provided the copy of Conquer Radio Frequency that was used to create this quiz, and has authorized me to include it in the monthly Book Drawing. His video to the right provides a great introduction to the book and to the very well-done set of instructional videos featured on the included DVD. AWR's Microwave Office (MWO) software is used throughout the tutorials. A live, narrated, step-by-step process is fully captured on-screen so you see how to create the circuit schematic, set up the component parameters for simulation and optimization, specify graph and table types, how to designate input files, configure input stimulus, and how to interpret the results of the simulation. It is an excellent way to familiarize yourself with where to find everything in MWO's menu and toolbar structure - which can be a daunting task with any sophisticated software. The book itself is chock full of very understandable instruction beginning with AC/RF fundamentals and progressing through impedance matching, transmission lines, Q factors, amplifier design, and much more. The illustrations are excellent.

1.  What mnemonic is used to determine the direction of a magnetic field around a current-carrying wire?

b)  The right-hand rule

Wrap your right hand around the wire with your thumb pointing in the direction of conventional current flow (see question #2). The direction your fingers wrap around the wire indicated the direction of the magnetic field encircling the wire.
(see page 5)

2.  What is conventional current flow?

a)  Current flowing from positive to negative

Before the nature of electron flow was known, scientists set a standard that current flowed out of the positive terminal of a source and back into the negative terminal. That is the definition of "conventional current flow." "Electron current flow" is from negative to positive.  (see page 5)

3.  What quantity (or quantities) does complex impedance indicate?

d)  Ratio of voltage to current amplitude and phase relationship

Complex impedance consists of a real (resistive) and an imaginary (reactive) component; i.e., Z = R ± jX. In the case of a pure resistance the imaginary component is zero; i.e., Z = R ± j0. In the case of a pure reactance the real component is zero; i.e, Z = 0 ± jX. The magnitude of the impedance, |Z|, is sqrt(R² + X²), and the phase angle, / X, is tan^-1(X/R).  (see page 25)

4.  What happens to the characteristic impedance of a coaxial transmission line when the dielectric constant of the space between the inner and outer conductor is increased?

a)  Impedance decreases

The equation governing characteristic impedance in a coaxial transmission line is Z₀ = (138/√εr)log(d_outer/d_inner) Ω  (see page 41)

5.  What portion of an incident signal is reflected by an open-circuit load and a short-circuit load, respectively?

d)  100% by the open circuit and 100% by the short circuit

With an open-circuit load no current can flow beyond the interface so all of the incident signal is reflected back toward the source. With a short-circuit load all current is shunted at the interface so all of the incident signal is also reflected back toward the source. The difference is that with an open circuit the reflected signal is in phase with the incident signal and with the short circuit the reflected signal is 180° out of phase with the incident signal. A way to conceptualize the situation is that in the case of the short circuit, in order for the voltage at the short to be zero (which it must be), the vector sum of the incident and reflected signals must be equal in amplitude and opposite in phase, hence they completely cancel. (see pages 75 - 85)

6.  How does the source "see" a 1/4-wavelength transmission line that is terminated in a short circuit?

c)  As an open circuit

Since a 1/4-wavelength transmission line is exactly the distance a signal of a specific frequency travels in 1/4th of its cycle period, the round-trip distance of a signal from the source to the load and back is 1/2 wavelength. Therefore, since a short circuit reflects the incident signal by 180°, and the length of the transmission line is also 1/2-wavelength, the total round-trip phase shift is 360°, hence, in-phase like an open circuit (ref. question 5).

(see page 97)

7.  How many degrees of phase change is represented by moving an impedance point all      the way around a constant impedance or constant admittance circle of a Smith Chart?

c)  180°

A way to conceptualize it is that the top half of the Smith Chart represents positive reactances (inductive, hence 0° to 90° of phase) and the bottom half of the chart represents negative reactances (capacitive, hence -90° to 0° of phase), the full range represents a total of -90° to 90°, or 180° of total phase change.  (see section 4.4.1)

8.  What is the phase relation of voltage and current in an ideal inductor?

b)  Voltage leads current by 90°

Since an inductor opposes an change in current flow, the full changing voltage in an AC signal assumes its new value across the inductor instantaneously while the current assumes its new value a quarter cycle later. Thus, the current lags the voltage (another way of saying the voltage leads the current). That reaction (hence "reactance") to an instantaneous change in current is due to the magnetic field associated with the inductor creating a counter EMF which opposes the current in proportion to dI/dt (V_inductor = LdI/dt). A single sinusoidal frequency component (per a Fourier series if not a pure tone) has as its first derivative the cosine, which leads by 90°. Just the opposite is true for a capacitor where the current leads the voltage. A commonly used mnemonic is ELI the ICE man, where E is voltage, L is inductance, I is current, and C is capacitance. By inspection, "E" (voltage) leads "I" (current) for "L" (inductance).  (see page 155)

9.  What is the meaning of unconditional stability for an amplifier circuit?

d)  The amplifier is not capable of oscillation at any phase of the source or load

Input and output stability circles plotted on a Smith Chart indicate the impedance regions, if any, within which the amplifier is capable of experiencing positive feedback from the output to the input and thereby going into oscillation. Those regions of instability can change with temperature, bias variations, signal impurities, or dynamically changing terminations, so margin is built into the design to allow for them. An old axiom illustrating the frustration of designing high frequency amplifier and oscillators (which are purposely designed with positive feedback to sustain oscillations) is, "If you want an amplifier, design an oscillator; if you want an oscillator, design an amplifier," meaning sometimes you can't stop an amplifier from oscillating and you can't get an oscillator to sustain oscillations. Such scenarios are prevented with the knowledgeable use of simulators like Microwave Office.  (see section 5.3.2)

10.  What are the three main stages of amplifier design?

a)  Biasing, stabilization, and impedance matching (see page 208)

Posted April 14, 2021