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The Voltage-Controlled Oscillator The frequency of a VFO can be adjusted by means of a varactor diode in the tuned LC circuit Recall that a varactor, also called a varicap, is a semiconductor diode that works as a variable capacitor when it is reverse-biased The capacitance depends on the reverse-bias voltage The greater this voltage, the lower the value of the capacitance The Hartley and Clapp oscillator circuits lend themselves well to varactor-diode frequency control The varactor is placed in series or parallel with the tuning capacitor, and is isolated for dc by blocking capacitors In Chap 20, we saw an example of how a varactor can be connected in a tuned circuit (Fig 20-9) The resulting oscillator is called a voltage-controlled oscillator (VCO) Varactors are cheaper than variable capacitors or inductors They re also less bulky These are the chief advantages of a VCO over an old-fashioned LC tuned VFO Diode Oscillators At ultrahigh frequencies (UHF) and microwave radio frequencies, certain types of diodes can be used as oscillators You learned about these diodes in Chap 20

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x 10 2 0 -2 x 10 2 0 -2 1 0 -1 1 0 -1 2 0 -2 0

Figure 114: Numeric solution of eqn (1188) with F from eqn (1190) showing the error response for a stationary INS initialized with 10 degree of east tilt error

One additional set of error conditions worth discussion is shown in Figure 115 This gure concerns an initial condition having 10 deg of azimuth error The simpli ed models of Section 1151 do not cover this situation However, assuming that the system is stationary, a reduced order model can be derived by considering the third and sixth rows of the system with the F matrix de ned in eqn (1190): vn E = 2 D ve g E 1 = vn D N + N Re (1193)

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Crystal-Controlled Oscillators Quartz crystals can be used in place of tuned LC circuits in RF oscillators, as long as it isn t necessary to change the frequency often Crystal oscillators offer frequency stability far superior to that of LC tuned VFOs There are several ways that crystals can be connected in bipolar or FET circuits to get oscillation One common circuit is the Pierce oscillator An N-channel JFET and quartz crystal are connected in a Pierce configuration as shown in the schematic diagram of Fig 24-16 The crystal frequency can be varied somewhat (by about 01 percent, or 1 part in 1000) by means of an inductor or capacitor in parallel with the crystal But the frequency is determined mainly by the thickness of the quartz wafer, and by the angle at which it is cut from the original quartz sample Crystals change in frequency as the temperature changes But they are far more stable than LC circuits, most of the time Some crystal oscillators are housed in temperature-controlled chambers called crystal ovens In this environment, crystals maintain their frequency so well that they are sometimes used as frequency standards against which other oscillators are calibrated The Phase-Locked Loop One type of oscillator that combines the flexibility of a VFO with the stability of a crystal oscillator is known as a phase-locked loop (PLL) This makes use of a circuit called a frequency synthesizer The heart of the PLL is a VCO The output of this oscillator passes through a programmable multiplier/divider, a digital circuit that divides and/or multiplies the VCO frequency by integral (whole-number) values chosen by the operator As a result, the output frequency can be any rationalnumber multiple of the crystal frequency A well-designed PLL circuit can be tuned in small digital increments over a wide range of frequencies The output frequency of the multiplier/divider is locked, by means of a phase comparator, to the signal from a crystal-controlled reference oscillator As long as the output from the multiplier/divider is exactly on the reference oscillator frequency, the two signals are in phase, and the output of the phase comparator is 0 V dc If the VCO frequency begins to drift, the output frequency of the multiplier/divider will drift, too (although at a different rate) But even a frequency change of less than 1 Hz causes the phase comparator to produce a dc error voltage This error voltage is either pos-.

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(1194)

phase-locked loop (PLL)

If the initial position and velocity errors are small and the tilt errors ( N and E ) can be accurately calibrated, then for the rst several minutes the error growth can be modeled as vn E = = g E 1 vn + N Re (1195)

D (0)

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