HETERODYNING

Information waveforms are produced by many different sources and are generally quite low in frequency. A good example is the human voice. The frequencies involved in normal speech vary from one individual to another and cover a wide range. This range can be anywhere from a low of about 90 hertz for a deep bass to as high as 10 kilohertz for a high soprano.

The most important speech frequencies almost entirely fall below 3 kilohertz. Higher frequencies merely help to achieve more perfect sound production. The range of frequencies used to transmit voice intelligence over radio circuits depends on the degree of FIDELITY (the ability to faithfully reproduce the input in the output) that is desired. The minimum frequency range that can be used for the transmission of speech is 500 to 2,000 hertz. The average range used on radiotelephone circuits is 250 to 2,750 hertz.

Frequencies contained within the human voice can be transmitted over telephone lines without difficulty, but transmitting them via radio circuits is not practical. This is because of their extremely long wavelengths and the fact that antennas would have to be constructed with long physical dimensions to transmit or radiate these wavelengths. Generally, antennas have radiating elements that are 1/4, 1/2, 1, or more full wavelengths of the frequency to be radiated. The wavelengths of voice frequencies employed on radiotelephone circuits range from 1,200,000 meters at 250 hertz to 109,090 meters at 2,750 hertz. Even a quarter-wave antenna would require a large area, be expensive to construct, and consume enormous amounts of power.

As studied in NEETS, Module 10, Introduction to Wave Propagation, Transmission Lines, and Antennas, radio frequencies do not have the limitations just described for voice frequencies. Radio waves, given a suitable antenna, can often radiate millions of miles into space. Several methods of modulation can be used to impress voices frequencies onto radio waves for transmission through space.

In the modulation process, waves from the information source are impressed onto a radio-frequency sine wave called a CARRIER. This carrier is sufficiently high in frequency to have a wavelength short enough to be radiated from an antenna of practical dimensions. For example, a carrier frequency of 10 megahertz has a wavelength of 30 meters, as shown below:

Construction of an antenna related to that wavelength does not cause any problems.

An information wave is normally referred to as a MODULATING WAVE. When a modulating wave is impressed on a carrier, the voltages of the modulating wave and the carrier are combined in such a manner as to produce a COMPLEX WAVE (a wave composed of two or more parts). This complex wave is referred to as the MODULATED WAVE and is the waveform that is transmitted through space. When the modulated wave is received and demodulated, the original component waves (carrier and modulating waves) are reproduced with their respective frequencies, phases, and amplitudes unchanged.

Modulation of a carrier can be achieved by any of several methods. Generally, the methods are named for the sine-wave characteristic that is altered by the modulation process. In this module, you will study AMPLITUDE MODULATION, which includes CONTINUOUS-WAVE MODULATION. You will also learn about two forms of ANGLE MODULATION (FREQUENCY MODULATION and PHASE MODULATION). A special type of modulation, known as PULSE MODULATION, will also be discussed. Before we present the methods involved in developing modulation, you need to study a process that is essential to the modulation of a carrier, known as heterodyning.

To help you understand the operation of heterodyning circuits, we will begin with a discussion of LINEAR and NONLINEAR devices. In linear devices, the output rises and falls directly with the input. In nonlinear devices, the output does not rise and fall directly with the input.

LINEAR IMPEDANCE

Whether the impedance of a device is linear or nonlinear can be determined by comparing the change in current through the device to the change in voltage applied to the device. The simple circuit shown in view (A) of figure 1-4 is used to explain this process.

Figure 1-4A. - Circuit with one linear impedance.

First, the current through the device must be measured as the voltage is varied. Then the current and voltage values can be plotted on a graph, such as the one shown in view (B), to determine the impedance of the device. For example, assume the voltage is varied from 0 to 200 volts in 50-volt steps, as shown in view (B). At the first 50-volt point, the ammeter reads 0.5 ampere. These ordinates are plotted as point a in view (B). With 100 volts applied, the ammeter reads 1 ampere; this value is plotted as point b. As these steps are continued, the values are plotted as points c and d. These points are connected with a straight line to show the linear relationship between current and voltage. For every change in voltage applied to the device, a proportional change occurs in the current through the device. When the change in current is proportional to the change in applied voltage, the impedance of the device is linear and a straight line is developed in the graph.

Figure 1-4B. - Circuit with one linear impedance.

The principle of linear impedance can be extended by connecting two impedance devices in series, as shown in figure 1-5, view (A). The characteristics of both individual impedances are determined as explained in the preceding section. For example, assume voltmeter V1 shows 50 volts and the ammeter shows 0.5 ampere. Point a in view (B) represents this ordinate. In the same manner, increasing the voltage in increments of 50 volts gives points b, c, and d. Lines Z1 and Z2 show the characteristics of the two impedances. The total voltage of the series combination can be determined by adding the voltages across Z1 and Z2. For example, at 0.5 ampere, point a (50 volts) plus point e (75 volts) produces point i (125 volts). Also, at 1 ampere, point b plus point f produces point j. Line Z1 + Z2 represents the combined voltage-current characteristics of the two devices.

Figure 1-5A. - Circuit with two linear impedances.

Figure 1-5B. - Circuit with two linear impedances.

View (A) of figure 1-6 shows two impedances in parallel. View (B) plots the impedances both individually (Z1 and Z2) and combined (Z1 x Z2)/(Z1 + Z2). Note that Z1 and Z2 are not equal. At 100 volts, Z1 has 1 ampere of current plotted at point b and Z2 has 0.5 ampere plotted at point f. The coordinates of the equivalent impedance of the parallel combination are found by adding the current through Z1 to the current through Z2. For example, at 100 volts, point b is added to point f to determine point j (1.5 amperes).

Figure 1-6. - Circuit with parallel linear impedances.

Positive or negative voltage values can be used to plot the voltage-current graph. Figure 1-7 shows an example of this situation. First, the voltage versus current is plotted with the battery polarity as shown in view (A). Then the battery polarity is reversed and the remaining voltage versus current points are plotted. As a result, the line shown in view (C) is obtained.

Figure 1-7A. - Linear impedance circuit.

Figure 1-7B. - Linear impedance circuit.

Figure 1-7C. - Linear impedance circuit

The battery in view (A) could be replaced with an ac generator, as shown in view (B), to plot the characteristic chart. The same linear voltage-current chart would result. Current flow in either direction is directly proportional to the change in voltage.

In conclusion, when dc or sine-wave voltages are applied to a linear impedance, the current through the impedance will vary directly with a change in the voltage. The device could be a resistor, an air-core inductor, a capacitor, or any other linear device. In other words, if a sine-wave generator output is applied to a combination of linear impedances, the resultant current will be a sine wave which is directly proportional to the change in voltage of the generator. The linear impedances do not alter the waveform of the sine wave. The amplitude of the voltage developed across each linear component may vary, or the phase of the wave may shift, but the shape of the wave will remain the same.