## 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.

A 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.

## From the trade magazines – 092612

Three more articles from recent editions of the electronics trade magazines.

Heathkit: A right-time, right-place business. Heathkit was a popular electronics company for decades before its demise earlier this year. Former employees Lou Frenzel and Chas Gilmore share some memories and discuss the factors that led to its closing. Lou Frenzel is W5LEF.

In the article, he notes how he was instrumental in developing the Heath/Zenith line of computer kits. At that time, I was a fledgling test engineer working for Memorex (remember them?) making the 8-in. floppy drives that were an option for those computers.

Real-world testing of wi-fi hotspots. This article talks about both the RF testing and data communications testing needed to ensure a good wi-fi hotspot.

How to simulate cable in SPICE. This article covers the two main loss effects related to cables (the skin effect and dielectric losses) and presents a simple cable modeling method for use in standard SPICE simulators.

## 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)

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)

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: 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: 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)

-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: 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

## From the trade magazines – September 14, 2012

Nikola Tesla slideshow: Images and articles from Tesla’s writings. This slideshow contains a sampling of images and excerpts from John Ratzlaff’s collection, which are all obtainable on the Internet. There are also several links to other awesome sites with info on Tesla.

Giga Sample and Direct-RF Sampling ADCs Overview. This video from TI demonstrates TI’s direct RF-sampling ADC IMD3 performance at 700 MHz and 2.7 GHz, allowing the elimination of one or more down-conversion stages. Features: sample rates up to 3.6 GSPS, dynamic performance up to 2.7 GHz inputs, largest high-res Nyquist zone at 1.8 GHz, and pin compatibility with TI’s 10- & 12-bit ADC families.

The basics of FPGA mathematics. For better performance, you can implement some digital signal processing (DSP) algorithms in an FPGA. This article takes a look at the rules and techniques that you can use to develop mathematical functions within an FPGA or other programmable device.

## Extra Class question of the day: Optical devices

Cathode-ray tubes (CRTs) used to the be most common type of display. They were not only used in television sets, but also computer terminals. They have an electron gun which shoots electrons onto a screen which then glows where the electron hits the screen. By sweeping this “beam” both horizontally and vertically, you can display an image on the screen.

To sweep the beam across the CRT, you deflect it by passing it though a set of plates. Varying the voltage will change the angle at which the beam is deflected. Electrostatic deflection is the type of CRT deflection that is better when high-frequency waveforms are to be displayed on the screen. (E6D13)

To accelerate the electron towards the screen, you apply a relatively high anode voltage to it. The higher the voltage, the brighter the CRT will glow. You don’t want to make that voltage too high, however. Exceeding the anode voltage specification can cause a cathode ray tube (CRT) to generate X-rays. (E6D02)

A spot on the CRT screen will glow even after the beam moves onto another spot. Cathode ray tube (CRT) persistence is the length of time the image remains on the screen after the beam is turned off. (E6D01) This characteristic is useful in many different applications.

A more modern type of display is the liquid-crystal display. A liquid-crystal display (LCD) is a display using a crystalline liquid which, in conjunction with polarizing filters, becomes opaque when voltage is applied. (E6D05) The principle advantage of liquid-crystal display (LCD) devices over other types of display devices is that they consume less power. (E6D15)

Unlike the CRT or LCD display, which transform electrical signals into an image, a charge-coupled device is used to transform an image into electrical signals. A charge-coupled device (CCD) samples an analog signal and passes it in stages from the input to the output. (E6D03) One of the things a charge-coupled device (CCD) does in a modern video camera is that it stores photogenerated charges as signals corresponding to pixels. (E6D04)One thing that is NOT true of a charge-coupled device (CCD) is that it is commonly used as an analog-to-digital converter. (E6D14)

## Extra Class question of the day: Modulation and demodulation

Modulation is the process of adding some kind of information, including voice and digital information, to a carrier signal. The most common types of modulation that we use in amateur radio are amplitude modulation (AM) and frequency modulation (FM). Single-sideband, or SSB, is a form of amplitude modulation.

To frequency modulate a carrier, a transmitter will sometimes us a modulator that varies the phase of the signal. This is sometimes called phase modulation (PM). One way to generate FM phone emissions is to use a reactance modulator on the oscillator. (E7E01) The function of a reactance modulator is to produce PM signals by using an electrically variable inductance or capacitance. (E7E02) An analog phase modulator functions by varying the tuning of an amplifier tank circuit to produce PM signals. (E7E03)

To boost the higher audio frequencies, a pre-emphasis network is often added to an FM transmitter. (E7E05) For compatibility with transmitters using phase modulation, de-emphasis is commonly used in FM communications receivers. (E7E06)

Amplitude modulation and single-sideband signals are produced using mixer circuits. The carrier frequency and the baseband signals are input to the mixer circuit which produces an amplitude modulated output. The term baseband in radio communications refers to the frequency components present in the modulating signal. (E7E07) The principal frequencies that appear at the output of a mixer circuit are the two input frequencies along with their sum and difference frequencies. (E7E08)

When using a mixer, you must take care not to use too high of a signal at the inputs. Spurious mixer products are generated when an excessive amount of signal energy reaches a mixer circuit. (E7E09)

Single sideband is most often used for phone transmission on the HF bands and for weak-signal operation on the VHF and UHF bands. One way a single-sideband phone signal can be generated is by using a balanced modulator followed by a filter.  (E7E04) A balanced modulator is a type of mixer.  The output of a balanced modulator, however, does not contain the carrier frequency, only the two sidebands.

Modern transceivers use digital signal processing to generate SSB signals. The quadrature method describes a common means of generating an SSB signal when using digital signal processing. (E7E13)

At the receiving station, a modulated signal has to be demodulated. Amplitude modulated signals are often demodulated using a diode detector circuit. A diode detector functions by rectification and filtering of RF signals. (E7E10)

For demodulating SSB signals, you want something a little more sophisticated. A product detector is a type of detector that is well suited for demodulating SSB signals. (E7E11) A product detector is actually a frequency mixer. It takes the product of the modulated signal and a local oscillator, hence the name. In an FM receiver, the circuit for detecting FM signals is a frequency discriminator. (E7E12)

Some modern receivers demodulate a signal entirely in software. These receivers are called software-defined receivers. When referring to a software defined receiver, direct conversion means incoming RF is mixed to “baseband” for analog-to-digital conversion and subsequent processing. (E7E14)