E8A02 (C)
What type of wave has a rise time significantly faster than its fall time (or vice versa)?
A. A cosine wave
B. A square wave
C. A sawtooth wave
D. A sine wave

E8A - AC waveforms: sine, square, sawtooth and irregular waveforms; AC measurements; average and PEP of RF signals; Fourier analysis; Analog to digital conversion: Digital to Analog conversion

We use all different kinds of waveforms in amateur radio. It is, therefore, important to know about the different types of waveforms and how to measure their parameters. One parameter of an AC waveform that you need to know is its root mean square, or RMS, value. The root-mean-square value of an AC voltage is the DC voltage causing the same amount of heating in a resistor as the corresponding RMS AC voltage. Because of this, the most accurate way of measuring the RMS voltage of a complex waveform would be measuring the heating effect in a known resistor. (E8A05)

If the waveform is regular, it’s relatively easy to calculate the RMS value. In the case of a sine wave, the RMS value is 0.707 times the peak value. You use the RMS voltage value to calculate the power of a wave.

The type of waveform produced by human speech is, however, irregular. For irregular waveforms, such as that of a single-sideband phone signal, we're most interested in the peak envelope power (PEP).

The characteristics of the modulating signal determine the PEP-to-average power ratio of a single-sideband phone signal. (E8A07) This makes calculating or measuring the average power more difficult.

If you know the peak envelope power (PEP), though, you can make a pretty good guess at the average power. The approximate ratio of PEP-to-average power in a typical single-sideband phone signal is 2.5 to 1. (E8A06) Put another way, the average power of an SSB signal is about 40% of the peak power.

It used to be that all the waveforms we used in amateur radio were analog waveforms, but nowadays digital waveforms may be even more important than analog waveforms. An advantage of using digital signals instead of analog signals to convey the same information is that digital signals can be regenerated multiple times without error. (E8A12)

All of these choices are correct when talking about the types of information that can be conveyed using digital waveforms (E8A11):

  • Human speech
  • Video signals
  • Data

Perhaps the most common digital wave form is the square wave. An ideal square wave alternates regularly and instantaneously between two different values. An interesting fact is that a square wave is the type of wave that is made up of a sine wave plus all of its odd harmonics. (E8A01)

Another type of wave used in amateur radio is the sawtooth wave. A sawtooth wave is the type of wave that has a rise time significantly faster than its fall time (or vice versa). (E8A02) The type of wave made up of sine waves of a given fundamental frequency plus all its harmonics is a sawtooth wave. (E8A03)

To make use of digital techniques in amateur radio, such as digital signal processing or DSP, we must convert analog signals to digital signals and vice-versa. To do this we use an analog-to-digital converter (ADC).

ADCs sample a signal at a particular point in time and convert that sample into a digital number that is proportional to the amplitude at that time. The number of bits in the digital number is called the resolution of the ADC. An analog-to-digital converter with 8 bit resolution can encode 256 levels. (E8A09)

To convert radio signals to digital streams used in software-defined radios, you need to sample the signal at a very high rate in order to preserve signal integrity. A direct or flash conversion analog-to digital converter would, therefore, be useful for a software defined radio because its very high speed allows digitizing high frequencies. (E8A08)

Sequential sampling is one of the methods commonly used to convert analog signals to digital signals. (E8A13) Sequential sampling allows you to sample a signal only once per cycle, thereby allowing you to use a slower, and less expensive ADC, and still preserve signal integrity. Sequential sampling only works, however, when the waveform is a regular waveform.

Sometimes signals are passed through a low pass filter before being digitized. The purpose of a low pass filter used in conjunction with a digital-to-analog converter is to remove harmonics from the output caused by the discrete analog levels generated. (E8A10)

The differential nonlinearity in the ADC’s encoder transfer function can be reduced by the proper use of dither. With respect to analog to digital converters, dither is a small amount of noise added to the input signal to allow more precise representation of a signal over time. (E8A04)






T-network filter

Figure E7C-1. T-network filter

This particular filter is a high-pass filter. That is to say it will pass frequencies above a certain frequency,

called the cutoff frequency, and block frequencies below that frequency. A T-network with series capacitors and a parallel shunt inductor has the property of it being a high-pass filter. (E7C02) The reason the circuit acts this way is that as the frequency of a signal increases, capacitive reactance decreases and inductive reactance increases, meaning that lower-frequency signals are more likely to be shunted to ground.

A circuit containing capacitors and inductors can also form a low-pass filter. A low-pass filter is a circuit that passes frequencies below the cutoff frequency and blocks frequencies above it.

Pi is the common name for a filter network which is equivalent to two L networks connected back-to-back with the inductors in series and the capacitors in shunt at the input and output. (E7C11). The circuit shown in figure E7C-2 is called a pi filter because it looks like the Greek letter π.

The capacitors and inductors of a low-pass filter Pi-network are arranged such that a capacitor is connected between the input and ground, another capacitor is connected between the output and ground, and an inductor is connected between input and output. (E7C01) The reason the circuit acts this way is that as the frequency of a signal increases, capacitive reactance decreases and inductive reactance increases, meaning that higher-frequency signals are more likely to be shunted to ground.

Pi-network filter

Figure E7C-2. Pi-network filter


Pi networks can also be used to match the output impedance of one circuit to the input impedance of another or the output impedance of a transmitter to the input impedance of an antenna. An impedance-matching circuit transforms a complex impedance to a resistive impedance because it cancels the reactive part of the impedance and changes the resistive part to a desired value .

(E7C04) One advantage of a Pi matching network over an L matching network consisting of a single inductor and a single capacitor is that the Q of Pi networks can be varied depending on the component values chosen. (E7C13)

A Pi network with an additional series inductor on the output describes a Pi-L network used for matching a vacuum-tube final amplifier to a 50-ohm unbalanced output. (E7C12) One advantage a Pi-L-network has over a Pi-network for impedance matching between the final amplifier of a vacuum-tube transmitter and an antenna is that it has greater harmonic suppression. (E7C03)

Piezoelectric crystals are also used to build filters. A crystal lattice filter is a filter with narrow bandwidth and steep skirts made using quartz crystals. (E7C15) 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. (E7C08) A "Jones filter" is a variable bandwidth crystal lattice filter used as part of a HF receiver IF stage. (E7C09)

Different types of filters have different characteristics. For example, a Chebyshev filter is a filter type described as having ripple in the passband and a sharp cutoff. (E7C05) On the other hand, the distinguishing features of an elliptical filter are extremely sharp cutoff with one or more notches in the stop band. (E7C06)

Filters have both amplitude and phase-response characteristics. In some applications, both are important. Digital modes, for example, are most affected by non-linear phase response in a receiver IF filter. (E7C14)

Often, you’ll choose a filter type for a particular application. For example, to attenuate an interfering carrier signal while receiving an SSB transmission, you would use a notch filter. (E7C07) A cavity filter would be the best choice for use in a 2 meter repeater duplexer. (E7C10)