Lecture 11 - 1 Lecture 11: Introduction to electronic...

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Lecture 11: Introduction to electronic analog circuits 361-1-3661 1 7.3. Oscillators for high frequencies: LC oscillators: Our aim is to develop oscillators with high frequency stability at high frequencies. We have to find a different approach because, as will be shown in the next lecture, the small-signal voltage gain decreases with frequency, and, therefore, the frequency stability of the Wien-bridge oscillator would be low at high frequencies. Our approach will be based on employing parallel RLC resonant circuits as feedback networks. (At high frequencies inductances are small and inexpensive.) The phase response of a resonant circuit is real at the frequency of resonance, and the phase condition of the Barkhausen criterion will hold true; hence, we will set the oscillator frequency at the resonant frequency of its feedback network: ω 1 = 0 . We saw in the previous lecture that to obtain high frequency stability the slope of the phase response of the feedback network, or its equivalent quality factor, should be high. By definition, equivalent quality factor, Q equiv , of a parallel resonant circuit equals its intrinsic quality factor: Q equiv = Q RLC =R /( 0 L ). Hence, to keep Q as high as possible for a given L and 0 we have to keep R as high as possible. Before starting the development of an oscillator, let us first see what the physical meaning of R is in a parallel resonant circuit. Fig. 1 shows that for a given , for example, 0 , R is inversely proportional to the resistance R' of the inductance wire: the lower R' : the higher R , the higher Q RLC . 7.3.1. Hartley and Colpitts oscillators According to the positive-feedback approach, we have to connect an amplifier to the RLC feedback network and to close the feedback loop to obtain an LC oscillator. In order not to reduce the quality factor of the RLC network, we have to choose only amplifiers with high output impedance. Otherwise, the output impedance of the amplifiers will shunt R in Fig. 1 and reduce Q RLC . Hence, we choose either CE or CB amplifiers. In a general case, the small-signal voltage gains of these amplifiers are greater than one. Therefore the transmission of the RLC feedback network at the resonant frequency should be less than unity to satisfy the amplitude condition of the Barkhausen criterion. This transmission should also be negative to satisfy the phase condition of the Barkhausen criterion for a CE amplifier and positive for a CB amplifier. These requirements can be met if we divide the voltage at the output of the RLC network as shown in Fig. 2. Without the reactive voltage divider in Fig. 2(b), the feedback network transmission at 1 = 0 would be equal to unity. This is so R' C L' R C L Re[ Ζ RLC ] Im[ RLC ] j 0 L' R' j 0 L R L f Q R Q R L f L f R 0 0 0 2 2 2 π = = = Fig. 1. A practical R'L'C circuit (above), a transformation of L' and R' into L and R (in the middle), and an electrical equivalent of the physical R'L'C circuit: a parallel RLC resonant circuit (below).
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Lecture 11 - 1 Lecture 11: Introduction to electronic...

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