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Design IdeasDecember 5, 1996 |
A simple technique provides phase
compensation for the oscillator in Figure 1a.
In this circuit, a tungsten lamp regulates the amplitude of a crystal bridge
oscillator. This type of oscillator produces a very low-distortion output at a
very stable frequency. The op amp must have a negligible phase shift at the
operating frequency, which is the series resonance frequency of the crystal. You
adjust RA to bring the output amplitude within the linear limits of
the op amp. At this point, the following relationship holds:
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The recent introduction of high-performance op amps, such as the AD8041 (Analog Devices, Norwood, MA) and EL2150 (Elantec, Milpitas, CA), permits this type of oscillator to operate at higher frequencies. However, even these high-speed devices introduce significant phase shifts. If you use the circuit in Figure 1a with a 5-MHz crystal, for example, it is impossible to reach a self-controlled and stable operating point. Figure 1b shows the simple addition of a compensating inductor, LC. LX is the inductance of the lamp, and you must measure this value before you can determine the proper value for LC.
Assume that at the operating frequency, the approximate gain of the amplifier is
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For the AD8041, this assumption is valid for frequencies as high as 10 MHz. Balancing the bridge leads to the following condition:
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This analysis ignores a term containing s2. For the practical values that Figure 1b uses, the corner frequencies of the denominators in the balancing equation (Equation 1) are an order of magnitude higher than those of the numerators, which leads to the following practical value for LC:
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Substituting the actual values from Figure 1b and from the AD8041's data sheet of Ao=30,000 and T=10 µsec produces an LC=0.4 µH. This inductor does not have to be precise; the nearest standard of value of 390 nH is acceptable. (DI #1957)
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