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Microwave Transistor Oscillator * One - port Negative - Resistance Oscillators Z in (V , w) Rin (V , w) jX in (V , w) amplitude and frequency - dependent and Rin (V , w) < 0 Z L ( w) RL ( w) jX L ( w) frequency - dependent The one - port network is stable if Re [ Z in (V , w) + Z L (w) ] > 0 The oscillation conditions : Rin (V , w) + RL (w) =0 X in (V , w) + X L (w) =0 At a specific frequency wO if the negative resistance | Rin (V , w) | > RL (w) and transient excitation => initiate an oscillation , then X L ( wO ) = - X in (V , wO ) Oscillation continue => the amplitude of the voltage eventually reach a steady - state Vo at this voltage Vo , the loop resistance is zero Rin (Vo, wo ) RL 0 and X in is amplitude dependent , X in (V1 , wO ) X in (VO , wO ) => This oscillation wO may not be stable . => a stable oscillation condition K . Kurokawa , “some basic characteristics of broadband negative resistance oscillator circuits , “ The Bell System Technical Journal , July 1969 . Summary : 1. The frequency of oscillation determined by X L ( wO ) = - X in (V , wO ) Rin (Vo, wo ) RL 0 2. Stable condition RIN (V , w) dX L ( w) X (V , w) dRL ( w) IN 0 V V VO dw wwO V V VO dw wwO Example 5.2.1 : A negative - resistance device can be modeled by the parallel combination of a capacitor and a negative conductance , as shown in Fig. 5.2.2a . The amplitude dependence of the negative conductance , shown in Fig. 5.2.2b is given by V G (V ) G M (1 ) (5.2.6) VM (a) (b) Figure 5.2.2 (a) Negative - resistance device ; (b) amplitude variations of G(V). Design a load circuit , Z L , to provide oscillation at wO and calculate the output power . Solution : The device impedance is G (V ) wC Z in (V , w) Rin (V , w) jX in (V , w) j 2 (5.2.7) G (V ) w C 2 2 2 G (V ) w 2 C 2 a stable oscillation at w wO occurs when G (V ) RL (5.2.8) G (V ) w 2 C 2 2 w wO ,V VO wC XL (5.2.9) G (V ) w 2C 2 2 w wO ,V VO RIN (V , w) dX L ( w) and 0 (5.2.10) V V VO dw wwO where VO is the oscillation voltage level at the frequency of oscillation wO . Substituting (5.2.6 ) into (5.2.7 ) gives for R IN , (1 / G M )(1 V / VM ) RIN (5.2.11) (1 V / VM ) 2 w 2 C 2 / G M 2 Differentiating (5.2.11 ) with respect to V gives RIN 1 2(V /VM ) V 2 /VM w 2C 2 / GM 2 2 (5.2.12) V GM VM [(1 V /VM ) 2 ( w2C 2 / GM )]2 2 and substituting (5.2.12) into (5.2.10) produces the relation dX L V V 2 w 2C 2 [ 1 2 2 2 ] 0 (5.2.13) dw w wO VM VM GM V V O There is no direct way to solve for R L and X L from (5.2.8) , (5.2.9) and (5.2.13) . Therefore , another design consideration such as maximizing the power delivered to R L must be introduced . The current in the circuit is given by I V ( G(V ) jwC) and the output power is given by 1 2 1 2 P I RL V RL (G 2 (V ) w 2 C 2 ) (5.2.14) 2 2 Substituting (5.2.6) and (5.2.8) into (5.2.14) gives 1 2 G (V ) 2 P VM (1 ) G (V ) (5.2.15) 2 GM The expression (5.2.15) can be maximized for G as follows : P 1 2 G(V ) G 2 (V ) VM [1 4 3 2 ]0 (5.2.15) G(V ) 2 GM GM G (V ) 1 or (5.2.16) GM 3 Substituting (5.2.16 ) into (5.2.6) gives V 2 (5.2.17) VM 3 which is the output voltage when maximum output power is delivered to RL . If (5.2.17) is evaluated at V VO and substituted back into (5.2.13) , the following result is obtained : dX L 2 wO C 2 1 ( 2 )0 (5.2.18) dw w wO GM 9 The only unknown in (5.2.18) is X L , so the frequency dependence of X L can easily be determined around wO are GM / 3 RL (5.2.19) (G M / 3) 2 wO C 2 2 wO C and X L ( wO ) (5.2.20) (G M / 3) 2 wO C 2 2 At this point , it is necessary to check if R L satisfies the condition (5.2.2) when the amplitude level is zero (i.e. the starting oscillation condition ) . Therefore , using (5.2.11) and (5.2.19) , we have that RIN (V , wO ) V 0 RL wO C 1 when GM 3 If we examine the ratio of R L to RIN (0, wO ) , we obtain RL 1 ( wO C / GM ) 2 3 (5.2.21) RIN (0, wO ) 1 9( wO C / GM ) 2 If wOC / GM is large , (5.2.21 ) can be approximated by RL 1 (5.2.22) R IN (0, wO ) 3 The relation (5.2.22) provides a good design guideline for selecting R L . That is , let 1 RL RIN (0, wO ) (5.2.23) 3 From (5.2.20) , the frequency of oscillation wO is 1 X L ( wO ) (5.2.24) wO C and from (5.2.18) dX L dw >0 (5.2.25) w wO Obviously , an inductor ( X L wL ) satisfies (5.2.24) and (5.2.25) , and wO is given by 1 wO LC Two - Port Negative Resistance Oscillators input port is oscillating when in L 1 1 1 S 22 T S12 S 21T L ( in S11 ) in S11 DT 1 S 22 T 1 S11L or T S 22 DL S S S D but out S 22 1 S 1 S 12 21 L 22 L 11 L 11 L out T 1 the terminating port is also oscillating Design produce for two - port oscillators 1. Use a potentially unstable transistor at the frequency of oscillation wO . 2. Design the terminating network to make IN 1 . Series or shunt feedback can be used to increase IN . 3. Design the load network to resonate Z IN . That is , let X L ( wO ) X IN ( wO ) (5.3.4) RIN (0, wO ) and RL (5.3.5) 3 Example 5.3.1 : Design an 8-GHz GaAs FET oscillator using the reverse - channel configuration shown in Fig. 5.5.4 . The S parameters of the transistor , in the reverse - channel configuration , at 8 GHz are S11 0.98163 0 S 21 0.675 161 0 S12 0.39 54 0 S 22 0.465 120 0 Ref1, P . C . Wade , “Novel FET Power Oscillators ,” Electronics Letters , Sep 1978 Ref2, P . C . Wade , “Say Hello to Power FET Oscillators ,”Microwaves , April 1979 Solution : The transistor is potentially unstable at 8GHz (i.e. K=0.529) and the stability circle at the gate - to - drain port is shown in Fig. In the notation of Fig. , the gate - to - drain port is the terminating port . As shown in Fig. , any T in the shaded region produces IN 1 (i.e. , a negative resistance at the input port). Selecting T at point A in Fig 5.3.2 (i.e. T = 1 163 ) , the associated impedance is Z T =-j7.5 . This 0 reactance can be implemented by an open - circuited 50- line of length 0.226 . With Z T connected , the input reflection coefficient is found to be IN 12 .8 16 .6 , and the associated impedance is Z IN 58 j 2.6 . 0 The load matching network is designed using Z L 19 j 2.6 at f O =8GHz . As reported in Refs. The oscillator was constructed and oscillated readily at frequencies between 7.5 and 7.8 GHz , with output power between 680 and 940Mw at VDS 9V . Some tuning was necessary to move the oscillation frequency to 8GHz . Example 5.3.2 : Design a 2.75 GHz oscillator using a BJT in a common - base configuration . The transistor S parameters at 2.75GHz are S11 0.9150 0 S 21 1.7 80 0 S12 0.07 120 0 S 22 1.08 56 0 (This example is based on a design from COMPACT reference manual .) Solution : The transistor is potentially unstable at 2.75GHz (K=-0.64) . The instability of the transistor can be increased using external feedback . For the common - base configuration (and also for the common - gate configuration ) a common lead inductance from base to ground (as shown in Fig. 5.3.3 ) is commonly used . Figure 5.3.3 BJT with external feedback to increase instability . Varying L from 0.5nH to 15nH , the resulting S parameters for the network in Fig. 5.3.3 are S11 1.72 100 0 S 21 2.08 136 0 S12 0.712 94 0 S 22 1.16 102 0 and K=-0.56 The common lead inductance has been used to raise S11 and S 22 to large values . Since S11 > S 22 , it appears that the emitter - to -ground port is the best place for the load network (i.e. the tuning network ) . Of course , these values are obtained with 50- terminations , and 50- terminations are not necessarily used for the matching networks . The terminating network can be designed to present an impedance to the collector having a real part smaller than 50 , and to couple the oscillator to a 50- termination . A design for the terminating network is illustrated , IN 2.21119 ( Z IN 24 j 24 .2 ) . From (5.3.4) and 0 in Fig. 5.3.4 (5.3.5) the impedance of the load matching network should be Z L 8 j 24 .2 . Figure 5.3.4 Terminating network design . Oscillator Configurations RF: Figure 5.5.1 Three types of common - base transistor configurations : (a) Clopitts (b) Hartley ; (c) Clapp. Microwave frequency : (bipolar oscillator) L is used to increase IN and out Figure 5.5.2 Common - base configuration. Low -Power circuits , easy to tune CE : also a popular choice for higher power oscillator Microwave frequency : (GaAs FET oscillator) Figure 5.5.3 (a) Common - gate configuration ; (b) common - source configuration . CG : for low power oscillator CS : for higher power oscillator Figure 5.5.4 Reverse - channel GaAs FET reverse - channel devices : a negative voltage applied to the drain terminal => the common lead inductance regenerative => S12 increases markedly with frequency and S11 greater than 1 in a large frequency range Load tuning element 1. LC 2. RLC 3. YIG resonator Figure 5.5.5 YIG -tuned oscillator . Figure 5.5.6 Equivalent network of a YIG sphere in a YIG -tuned oscillator. 4. Varactor Figure 5.5.7 Varactor - tuned oscillator. CO varactor diode model Cv V 1 (1 ) 2 Rr V Cv Rs

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Oscillator Design, Transistor Oscillator, microwave circuits, Microwave Transistor Amplifiers, phase noise, RF and Microwave Oscillator Design, Microwave designers, Radio Frequency, communications applications, consumer electronics

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posted: | 3/27/2010 |

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