Extra Class question of the day: Smith Chart

NOTE: This is the last installment of the Extra Class question of the day. I’m going to be compiling all of these into the No-Nonsense Extra Class Study Guide. Watch for it real soon now.


Figure E9-3A Smith chart is shown in Figure E9-3 above. (E9G05) It is a chart designed to solve transmission line problems graphically. While a complete discussion of the theory behind the Smith Chart is outside the scope of this study guide, a good discussion of the Smith Chart can be found on the ARRL website.

The coordinate system is used in a Smith chart is comprised of resistance circles and reactance arcs. (E9G02) Resistance and reactance are the two families of circles and arcs that make up a Smith chart. (E9G04)

The resistance axis is the only straight line shown on the Smith chart shown in Figure E9-3. (E9G07) Points on this axis are pure resistances. In practice, you want to position the chart so that 0 ohms is at the far left, while infinity is at the far right.

The arcs on a Smith chart represent points with constant reactance. (E9G10) On the Smith chart, shown in Figure E9-3, the name for the large outer circle on which the reactance arcs terminate is the reactance axis. (E9G06) Points on the reactance axis have a resistance of 0 ohms. When oriented so that the resistance axis is horizontal, positive reactances are plotted above the resistance axis and negative reactances below.

The process of normalization with regard to a Smith chart refers to reassigning impedance values with regard to the prime center. (E9G08) The prime center is the point marked 1.0 on the resistance axis. If you’re working with a 50 ohm transmission line, you’d normally divide the impedances by 50, meaning that a 50 ohm resistance would then be plotted on the resistance axis at the point marked 1.0. A reactance of 50 + j100 would be plotted on the resistance circle going through the prime center where it intersects the reactance arc marked 2.0.

Impedance along transmission lines can be calculated using a Smith chart. (E9G01) Impedance and SWR values in transmission lines are often determined using a Smith chart. (E9G03) Standing-wave ratio circles are often added to a Smith chart during the process of solving problems. (E9G09)

The wavelength scales on a Smith chart calibrated in fractions of transmission line electrical wavelength. (E9G11) These are useful when trying to determine how long transmission lines must be when used to match a load to a transmitter.

Extra Class question of the day: Amplifiers

There are several classifications of amplifiers, based on their mode of operation. In a class A amplifier is always conducting current. That means that the bias of a Class A common emitter amplifier would normally be set approximately half-way between saturation and cutoff on the load line. (E7B04)

In a class B amplifer, there are normally two transistors operating in a “push-pull” configuration. One transistor turns on during the positive half of a cycle, while the other turns on during the negative half. Push-pull amplifiers reduce or eliminate even-order harmonics. (E7B06)

A Class AB amplifier operates over more than 180 degrees but less than 360 degrees of a signal cycle. (E7B01) Class B and Class AB amplifiers are more efficient than Class A amplifiers.

A Class D amplifier is a type of amplifier that uses switching technology to achieve high efficiency. (E7B02) The output of a class D amplifier circuit includes a low-pass filter to remove switching signal components. (E7B03)

Amplifiers are used in many different applications, but one application that is especially important, at least as far as signal quality goes, is RF power amplification. RF power amplifiers may emit harmonics or spurious signals, that may cause harmful interference.

One thing that can be done to prevent unwanted oscillations in an RF power amplifier is to install parasitic suppressors and/or neutralize the stage. (E7B05) An RF power amplifier be neutralized by feeding a 180-degree out-of-phase portion of the output back to the input. (E7B08) Another thing one can do to reduce unwanted emissions is to use a push-pull amplifier. Signal distortion and excessive bandwidth is a likely result when a Class C amplifier is used to amplify a single-sideband phone signal. (E7B07)

While most modern transceivers use transistors in their final amplifiers, and the output impedance is 50 ohms over a wide frequency range. A field effect transistor is generally best suited for UHF or microwave power amplifier applications. (E7B21)

Many high-power amplifiers, however, still use vacuum tubes. These amplifiers require that the operator tune the output circuit. The tuning capacitor is adjusted for minimum plate current, while the loading capacitor is adjusted for maximum permissible plate current is how the loading and tuning capacitors are to be adjusted when tuning a vacuum tube RF power amplifier that employs a pi-network output circuit. (E7B09)

Figure E7-1

The type of circuit shown in Figure E7-1 is a common emitter amplifier. (E7B12) In Figure E7-1, the purpose of R1 and R2 is to provide fixed bias. (E7B10) In Figure E7-1, what is the purpose of R3  is to provide self bias. (E7B11)

Figure E7-2

In Figure E7-2, the purpose of R is to provide emitter load. (E7B13) In Figure E7-2, the purpose of C2 is to provide output coupling. (E7B14)

Thermal runaway is one problem that can occur if a transistor amplifier is not designed correctly. What happens is that when the ambient temperature increases, the leakage current of the transistor increases, causing an increase in the collector-to-emitter current. This increases the power dissipation, further increasing the junction temperature, which increases yet again the leakage current. One way to prevent thermal runaway in a bipolar transistor amplifier is to use a resistor in series with the emitter. (E7B15)

RF power amplifers often generate unwanted signals via a process called intermodulation. Strong signals external to the transmitter combine with the signal being generated, causing sometimes unexpected and unwanted emissions. The effect of intermodulation products in a linear power amplifier is the transmission of spurious signals. E7B16() Third-order intermodulation distortion products are of particular concern in linear power amplifiers because they are relatively close in frequency to the desired signal. (E7B17)

Finally, there are several questions on special-application amplifiers. A klystron is a VHF, UHF, or microwave vacuum tube that uses velocity modulation. (E7B19) A parametric amplifier is a low-noise VHF or UHF amplifier relying on varying reactance for amplification. (E7B20)

Extra Class question of the day: Direction finding

Direction finding is an activity that’s both fun and useful. One of the ways that it’s useful is to hunt down noise sources. It can also be used to hunt down stations causing harmful interference.

A variety of directional antennas are used in direction finding, including the shielded loop antenna. A receiving loop antenna consists of one or more turns of wire wound in the shape of a large open coil. (E9H09) The output voltage of a multi-turn receiving loop antenna be increased by increasing either the number of wire turns in the loop or the area of the loop structure or both. (E9H10)

An advantage of using a shielded loop antenna for direction finding is that it is electro-statically balanced against ground, giving better nulls. (E9H12) The main drawback of a wire-loop antenna for direction finding is that it has a bidirectional pattern. (E9H05)

Sometimes a sense antenna is used with a direction finding antenna. The function of a sense antenna is that it modifies the pattern of a DF antenna array to provide a null in one direction. (E9H08)

Another way to obtain a null in only one direction is to build an antenna array with a cardioid pattern. One way to do this is to build an array with two dipoles fed in quadrature. A very sharp single null is a  characteristic of a cardioid-pattern antenna is useful for direction finding. (E9H11)

Another accessory that is often used in direction finding is an attenuator. It is advisable to use an RF attenuator on a receiver being used for direction finding because it prevents receiver overload which could make it difficult to determine peaks or nulls. (E9H07)

If more than one operator can be mobilized for a direction-finding operation, they could use the triangulation method for finding a noise source or the source of a radio signal. When using the triangulation method of direction finding, antenna headings from several different receiving locations are used to locate the signal source. (E9H06)

Extra Class question of the day: Effective radiated power

Effective radiated power is a widely misunderstood concept. Effective radiated power is the term that describes station output, including the transmitter, antenna and everything in between, when considering transmitter power and system gains and losses. (E9H04)

The effective radiated power, or ERP, is always given with respect to a certain direction. Let’s think about this for a second. If your transmitter has an output of 100 W, the maximum power that the antenna can radiate is also 100 W. Transmitting antennas are, after all, passive devices. You can’t get more power out of them that you put into them. In reality, the total power output will be even less than 100 W because you will have losses in the feedline.

An antenna can, however, concentrate the power in a certain direction. The power being radiated in that direction will be more than the power radiated in that direction by a reference antenna, usually a dipole or an isotropic antenna, which is an antenna that radiates equally in all directions.

When an antenna concentrates power in a certain direction, we say that it has gain in that direction, and we specify the amount of gain in dB. If the reference antenna is an isotropic antenna, then the unit of gain is dBi. If the reference antenna is a dipole, then the unit of gain is dBd.

With that in mind, let’s take a look at an example. In this example, a repeater station has 150 watts transmitter power output, there is a 2-dB feed line loss, 2.2-dB duplexer loss, and the antenna has 7-dBd gain. To calculate the system gain (or loss), you add the gains and losses, so

Gain = 7 dBd – 2 dB – 2.2 dB = + 2.8 dB

dB Ratio
1 1.26:1
2 1.585:1
3 2:1

Now, if you recall, 3 dB is close to a gain of 2, as shown in the table at right, so in this example, to calculate the effective radiated power, you multiply the transmitter’s output power by a factor slightly less than two. This makes the effective radiated power slightly less than 15o W x 2, or 300 W. The closest answer to 300 W is 286 W. (E9H01)

Let’s look at another example. The effective radiated power relative to a dipole of a repeater station with 200 watts transmitter power output, 4-dB feed line loss, 3.2-dB duplexer loss, 0.8-dB circulator loss and 10-dBd antenna gain is 317 watts. (E9H02) In this example, the gain is equal to 10 dB – 8 dB in lossses or a net gain of 2 dB. That’s equivalent to a ratio of 1.585:1. The ERP is then 200 W x 1.585 = 317 W.

Now, lets look at an example using an isotropic antenna as the reference antenna. The effective isotropic radiated power of a repeater station with 200 watts transmitter power output, 2-dB feed line loss, 2.8-dB duplexer loss, 1.2-dB circulator loss and 7-dBi antenna gain is 252 watts. (E9H03) In this example, the gain is equal to 7 dB – 2 dB – 2.8 dB – 1.2 dB = 1 dB. That’s equivalent to a ratio of 1.26:1, so the ERP is 200 W x 1.26 = 252 W.

Extra Class question of the day: Frequency counters and markers

To measure the frequency of a signal, you use an instrument called a frequency counter. The purpose of a frequency counter is to provide a digital representation of the frequency of a signal.(E7F09) A frequency counter counts the number of input pulses occurring within a specific period of time. (E7F08)

To accurately measure high-frequency signals digitally, you need a highly stable and accurate frequency source, called the time base. The time base provides an accurate and repeatable time period, over which you count the number of pulses of the test signal. The accuracy of the time base determines the accuracy of a frequency counter. (E7F07)

An alternate method of determining frequency, other than by directly counting input pulses, that is used by some counters is period measurement plus mathematical computation. (E7F10) An advantage of a period-measuring frequency counter over a direct-count type is that it provides improved resolution of low-frequency signals within a comparable time period. (E7F11)

You also need an accurate and stable time base to generate and receive microwave signals. All of these choices are correct when talking about techniques for providing high stability oscillators needed for microwave transmission and reception: (E7F05)

  • Use a GPS signal reference
  • Use a rubidium stabilized reference oscillator
  • Use a temperature-controlled high Q dielectric resonator

If you want to measure a signal whose frequency is higher than the maximum frequency of your counter, you might use a prescaler. The purpose of a prescaler circuit is to divide a higher frequency signal so a low-frequency counter can display the input frequency. (E7F01) A prescaler would, for example, be used to reduce a signal’s frequency by a factor of ten. (E7F02)

You might use a decade counter digital IC in a prescaler circuit. The function of a decade counter digital IC is to produce one output pulse for every ten input pulses. (E7F03)

In some cases, you might use a flip-flop. Two flip-flops must be added to a 100-kHz crystal-controlled marker generator so as to provide markers at 50 and 25 kHz. (E7F04) The purpose of a marker generator is to provide a means of calibrating a receiver’s frequency settings. (E7F06) You mostly find marker generators in older, analog receivers.

Extra Class question of the day: Wire and phased vertical antennas

There are many ways to put up antennas that are directional. Yagis are directional antennas, but they require a structure, such as a tower, to get them high in the air. One way to get directionality without a tower is to use phased vertical arrays.

In general, the phased vertical array consists of two or more quarter-wave vertical antennas. The radiation pattern that the array will have depends on how you feed the vertical antennas.

So, for example, the radiation pattern of two 1/4-wavelength vertical antennas spaced 1/2-wavelength apart and fed 180 degrees out of phase is a figure-8 oriented along the axis of the array. (E9C01) The radiation pattern of two 1/4-wavelength vertical antennas spaced 1/4-wavelength apart and fed 90 degrees out of phase is a cardioid. (E9C02) The radiation pattern of two 1/4-wavelength vertical antennas spaced 1/2-wavelength apart and fed in phase is a Figure-8 broadside to the axis of the array. (E9C03)

A rhombic antenna is often used for receiving on the HF bands. A basic unterminated rhombic antenna is described as bidirectional; four-sides, each side one or more wavelengths long; open at the end opposite the transmission line connection. (E9C04) The disadvantages of a terminated rhombic antenna for the HF bands is that the antenna requires a large physical area and 4 separate supports. (E9C05) Putting a terminating resistor on a rhombic antenna changes the radiation pattern from bidirectional to unidirectional. (E9C06)

Figure E9-2: Elevation Pattern

The type of antenna pattern over real ground that is shown in Figure E9-2 is an elevation pattern. (E9C07) The elevation angle of peak response in the antenna radiation pattern shown in Figure E9-2 is 7.5 degrees. (E9C08) The front-to-back ratio of the radiation pattern shown in Figure E9-2 is 28 dB. (E9C09) 4 elevation lobes appear in the forward direction of the antenna radiation pattern shown in Figure E9-2. (E9C10)

How and where you install an antenna affects its radiation pattern. For example, the far-field elevation pattern of a vertically polarized antenna is affected when it is mounted over seawater versus rocky ground. What happens is that the low-angle radiation increases. (E9C11) The main effect of placing a vertical antenna over an imperfect ground is that it reduces low-angle radiation. (E9C13) When constructing a Beverage antenna, remember that it should be one or more wavelengths long to achieve good performance at the desired frequency. (E9C12)

Extra Class question of the day: Piezoelectric crystals and MMICs

Piezoelectric crystals are used in several amateur radio applications. They are called piezoelectric crystals because they use the piezoelectric effect, which is the physical deformation of a crystal by the application of a voltage. (E6E03) The equivalent circuit of a quartz crystal consist of motional capacitance, motional inductance and loss resistance in series, with a shunt capacitance representing electrode and stray capacitance. (E6E10)

Perhaps the most common use for a piezoelectric crystal is as the frequency-controlling component in an oscillator circuit. To ensure that a crystal oscillator provides the frequency specified by the crystal manufacturer, you must provide the crystal with a specified parallel capacitance. (E6E09)

Piezoelectric crystals are also used in crystal filters. A crystal lattice filter is a filter with narrow bandwidth and steep skirts made using quartz crystals. (E6E01) The relative frequencies of the individual crystals is the factor that has the greatest effect in helping determine the bandwidth and response shape of a crystal ladder filter. (E6E02) A “Jones filter” is a variable bandwidth crystal lattice filter used as part of a HF receiver IF stage. (E6E12)

Monolithic microwave integrated circuits, or MMICs, are ICs that are made to perform various functions at high frequencies. Gallium nitride is the material that is likely to provide the highest frequency of operation when used in MMICs. (E6E11)

The characteristics of the MMIC that make it a popular choice for VHF through microwave circuits are controlled gain, low noise figure, and constant input and output impedance over the specified frequency range. (E6E06) For example, a low-noise UHF preamplifier might have a typical noise figure value of 2 dB. (E6E05) 50 ohms is the most common input and output impedance of circuits that use MMICs. (E6E04)

To achieve these specifications, great care is taken in building and using an MMIC. For example, microstrip construction is typically used to construct a MMIC-based microwave amplifier. (E6E07) The power-supply voltage is normally furnished to the most common type of monolithic microwave integrated circuit (MMIC) through a resistor and/or RF choke connected to the amplifier output lead. (E6E08)

Extra Class question of the day: Operational amplifiers

An integrated circuit operational amplifier is a high-gain, direct-coupled differential amplifier with very high input and very low output impedance. (E7G12) They are very versatile components. They can be used used to build amplifiers, filter circuits, and many other types of circuits that do analog signal processing.

Because they are active components–that is to say that they amplify–filters made with op amps are called active filters. The most appropriate use of an op-amp active filter is as an audio filter in a receiver. (E7G06). An advantage of using an op-amp instead of LC elements in an audio filter is that op-amps exhibit gain rather than insertion loss. (E7G03)

The values of capacitors and resistors external to the op-amp primarily determine the gain and frequency characteristics of an op-amp RC active filter. (E7G01) The type of capacitor best suited for use in high-stability op-amp RC active filter circuits is polystyrene. (E7G04) Polystyrene capacitors are used in applications where very low distortion is required.

Ringing in a filter may cause undesired oscillations to be added to the desired signal. (E7G02) One way to prevent unwanted ringing and audio instability in a multi-section op-amp RC audio filter circuit is to restrict both gain and Q. (E7G05)

Calculating the gain of an op amp circuit is relatively straightforward. The gain is simply RF/Rin. In figure E7-4 below, Rin  = R1. Therefore, the magnitude of voltage gain that can be expected from the circuit in Figure E7-4 when R1 is 10 ohms and RF is 470 ohms is 470/10, or 47. (E7G07) The absolute voltage gain that can be expected from the circuit in Figure E7-4 when R1 is 1800 ohms and RF is 68 kilohms is 68,000/1,800, or  38. (E7G10) The absolute voltage gain that can be expected from the circuit in Figure E7-4 when R1 is 3300 ohms and RF is 47 kilohms is 47,000/3,300, or 14. (E7G11)

Figure E7-4. Operational amplifier circuit

-2.3 volts will be the output voltage of the circuit shown in Figure E7-4 if R1 is 1000 ohms, RF is 10,000 ohms, and 0.23 volts dc is applied to the input. (E7G09) The gain of the circuit will be 10,000/1,000 or 10, and the output voltage will be equal to the input voltage times the gain. 0.23 V x 10 = 2.3 V, but since the input voltage is being applied to the negative input, the output voltage will be negative.

Two characteristics that make op amps desirable components is their input impedance and output impedance. The typical input impedance of an integrated circuit op-amp is very high. (E7G14) This feature makes them useful in measurement applications. The typical output impedance of an integrated circuit op-amp is very low. (E7G15)

The gain of an ideal operational amplifier does not vary with frequency.  (E7G08) Most op amps aren’t ideal, though. While some modern op amps can be used at high frequencies, many of the older on the older ones can’t be used at frequencies above a couple of MHz.

Ideally, with no input signal, there should be no voltage difference between  the two input terminals. Since no electronic component is ideal, there will be a voltage between these two terminals. We call this the input offset voltage. Put another way, the op-amp input-offset voltage is the differential input voltage needed to bring the open-loop output voltage to zero. (E7G13)

Extra Class question of the day: Miscellaneous rules

As the name of this section implies, it contains a hodgepodge of questions covering sometimes obscure rules. About the only way to get these right is to memorize the answers.

The use of spread-spectrum techniques is a topic that comes up from time to time. Many amateurs feel that the rules are too restrictive. For example, 10 W is the maximum transmitter power for an amateur station transmitting spread spectrum communications. (E1F10) Only on amateur frequencies above 222 MHz are spread spectrum transmissions permitted. (E1F01)

All of these choices are correct when talking about the conditions that apply when transmitting spread spectrum emission: (E1F09)

  • A station transmitting SS emission must not cause harmful interference to other stations employing other authorized emissions.
  • The transmitting station must be in an area regulated by the FCC or in a country that permits SS emissions.
  • The transmission must not be used to obscure the meaning of any communication.

The rules governing the use of external amplifiers is also somewhat controversial. A dealer may sell an external RF power amplifier capable of operation below 144 MHz if it has not been granted FCC certification if it was purchased in used condition from an amateur operator and is sold to another amateur operator for use at that operator’s station. (E1F03) One of the standards that must be met by an external RF power amplifier if it is to qualify for a grant of FCC certification is that it must satisfy the FCC’s spurious emission standards when operated at the lesser of 1500 watts, or its full output power. (E1F11)

There are some rules that spell out restrictions based on where a station is located. For example, amateur radio stations may not operate in the National Radio Quiet Zone. The National Radio Quiet Zone is an area surrounding the National Radio Astronomy Observatory. (E1F06) The NRAO is located in Green Bank, West Virginia.

There is also a regulation that protects Canadian Land/Mobile operations near the US/Canadian border from interference. Amateur stations may not transmit in the 420 – 430 MHz frequency segment if they are located in the contiguous 48 states and north of Line A. (E1F05) A line roughly parallel to and south of the US-Canadian border describes “Line A.” (E1F04) There is a corresponding “Line B” parallel to and north of the U.S./Canadian border.

As you might expect, there are some questions about not making any money from operating an amateur radio station. Communications transmitted for hire or material compensation, except as otherwise provided in the rules are prohibited. (E1F08) An amateur station may send a message to a business only when neither the amateur nor his or her employer has a pecuniary interest in the communications. (E1F07)

This next question is a bit of a trick question. 97.201 states that only Technician, General, Advanced or Amateur Extra Class operators may be the control operator of an auxiliary station. (E1F12) It’s a trick question because there are also holders of Novice Class licenses even though no new Novice licenses have been issued for many years, and the number of Novice Class licensees dwindles every year.

Communications incidental to the purpose of the amateur service and remarks of a personal nature are the types of communications may be transmitted to amateur stations in foreign countries. (E1F13)

The FCC might issue a “Special Temporary Authority” (STA) to an amateur station to provide for experimental amateur communications. (E1F14)

The CEPT agreement allows an FCC-licensed US citizen to operate in many European countries, and alien amateurs from many European countries to operate in the US. (E1F02)

Extra Class question of the day: Toroids

Toroidal inductors are very popular these days. A primary advantage of using a toroidal core instead of a solenoidal core in an inductor is that toroidal cores confine most of the magnetic field within the core material. (E6D10)

Another reason for their popularity is the frequency range over which you can use them. The usable frequency range of inductors that use toroidal cores, assuming a correct selection of core material for the frequency being used is from less than 20 Hz to approximately 300 MHz. (E6D07) Ferrite beads are commonly used as VHF and UHF parasitic suppressors at the input and output terminals of transistorized HF amplifiers. (E6D09)

An important characteristic of a toroid core is its permeability. Permeability is the core material property that determines the inductance of a toroidal inductor. (E6D06)

One important reason for using powdered-iron toroids rather than ferrite toroids in an inductor is that powdered-iron toroids generally maintain their characteristics at higher currents. (E6D08) One reason for using ferrite toroids rather than powdered-iron toroids in an inductor is that ferrite toroids generally require fewer turns to produce a given inductance value. (E6D16)

To calculate the inductance of a ferrite-core toroid, we need the inductance index of the core material. The formula that we use to calculate the inductance of a ferrite-core toroid inductor is:

L = AL×N2/1,000,000

where L = inductance in microhenries, AL = inductance index in µH per 1000 turns, and N = number of turns

We can solve for N to get the following formula:

N = 1000 x sqrt (L/AL)

Using that equation, we see that 43 turns will be required to produce a 1-mH inductor using a ferrite toroidal core that has an inductance index (A L) value of 523 millihenrys/1000 turns. (E6D11)

N = 1000 x sqrt (1/523) = 1000 x .0437 = 43.7 turns

The formula for calculating the inductance of a powdered-iron core toroid inductor is:

L = AL×N2/10,000

where L = inductance in microhenries, AL = inductance index in µH per 1000 turns, and N = number of turns

We can solve for N to get the following formula:

N = 100 x sqrt (L/AL)

Using that equation, we calculate that 35 turns turns will be required to produce a 5-microhenry inductor using a powdered-iron toroidal core that has an inductance index (A L) value of 40 microhenrys/100 turns. (E6D12)

N = 1000 x sqrt (5/40) = 100 x .353 = 35.3 turns