Lecture 33 Active Microwave Circuits: Two-Port Power Gains.

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1 Whites, EE 481/581 ecture 33 age 1 of 11 ecture 33 Active Microwave Circuits: Two-ort ower Gas. We are gog to focus on active microwave circuits for the remader of the semester. There are many types of active circuits such as amplifiers, oscillators, and mixers. We will concentrate only on amplifiers. It is often a much more volved process to design and construct active circuits that operate correctly than passive ones. Reasons for this clude: A bias network is required, The devices are nonlear, Untended oscillations produced by circuit stability. More care, patience, and experience are often required the design of active RF and microwave circuits than purely passive ones. The analysis of such circuits is usually very difficult given the nonlear behavior of the devices. For lear amplifiers, though, a lear analysis is applicable, which helps simplify matters. For this reason, we will focus on lear, small signal amplifiers. Furthermore, we will use measured (or given) parameters for the devices (transistors) rather than detailed device parameters (β, C, r, etc.). Consequently, we can treat the transistor as a 015 Keith W. Whites

2 Whites, EE 481/581 ecture 33 age of 11 two port, but possibly one with ga. This approach works well for the steady state analysis of lear, small-signal amplifiers. For other types of active circuits, such as oscillators, mixers, or power amplifiers, the nonlear behavior of the circuit devices must be explicitly accounted for, which precludes the use of parameters. Much more difficult. One big difference with active devices is that the magnitude of the parameters may be greater than one. Often it is only 1 that has this characteristic, with port 1 servg as the put and port the put. With passive devices, parameters with magnitudes greater than unity are physically impossible. Types of ower Gas Referrg to a generic two-port network circuit such as Z 0 Z 0 there are three commonly used defitions for power ga. 1. Operatg ower Ga: G (1)

3 Whites, EE 481/581 ecture 33 age 3 of 11 This is the ratio of the time-average power dissipated a load to the time-average power delivered to the network. av, n. Available Ga: GA () av, This is the ratio of the maximally available time-average power from the network to the maximally available timeaverage power from the source. 3. Transducer Ga: GT (3) av, This is the ratio of the time-average power dissipated the load to the maximally available time-average power from the source. It is this latter transducer ga that you used EE 3 Electronics II Wireless Communication Electronics to characterize the performance (i.e. ga) of the active devices circuits. Among other applications, these three defitions of power ga are used to design different types of amplifiers: 1. Operatg ower Ga, G. Maximum lear put power amplifiers.. Available ower Ga, G A. ow Noise Amplifiers (NAs).

4 Whites, EE 481/581 ecture 33 age 4 of Transducer ower Ga, G T. imultaneously conjugate matched put and put ports (leads to maximum lear ga). ower Ga Expressions We will now derive analytical expressions for these power gas terms of the parameters of the network, as well as the source and load impedances. These will prove central to the design of lear microwave amplifiers. Referrg to this generic two-port circuit (Fig. 1.1): V + - Z + V- 1 V 1 t1 t [] (wrt Z 0 ) V Z Z V 1 V Ts are fitesimally short, with characteristic impedance Z 0. Z then by the defition of the parameters we can write V V V (1.a),(4) and V 1V1 V (1.b),(5) In these equations we have used the relationship V V. As we showed ecture 1 usg signal flow graphs

5 Whites, EE 481/581 ecture 33 age 5 of 11 V (1.3a),(6) V1 1 imilarly, it can be show that V 11 (1.3b),(7) V 1 11 Next, by voltage division at the source and for an fitesimally short T Z V1 V V1 V1 V1 1 Z Z (8) so that Z V V 1 Z Z 1 (9) Now, usg Z Z Z Z 0 0 and after some algebra, (9) can be reduced to 1 V V 1 (1.4),(10) 1 There are four different time-average power quantities we need to determe order to compute (1)-(3): 1. : Time-average power provided by the source V1 1 (1.5),(11) Z0 ubstitutg for V 1 from (10) gives

6 Whites, EE 481/581 ecture 33 age 6 of 11 V Z0 1 (1.5),(1). : Time-average power delivered to the load. This quantity is similar to (11): V 1 (1.6),(13) Z Usg (5) and (10) (13), as shown the text, V Z (1.7),(14) 3. av,s : Maximum available power from the source (and * * supplied to the circuit). This occurs when Z Z * (i.e., conjugate match). o, from (1) and with : V 1 1 av, * 8 Z 1 But with 1 1 then 0 V 1 av, 8Z0 1 (1.9),(15) 4. av,n : Maximum available power from the network (and supplied to the load). This occurs when * * Z Z (i.e., conjugate match). From (14) * and with :

7 Whites, EE 481/581 ecture 33 age 7 of 11 V av, n * 1 * 8 Z Usg (6) and after considerable algebra, it can be shown that V 1 av, n 1 (1.11),(16) 8 Z With these four time-average power quantities (1) and (14)- (16), we are now a position to compute the three power ga expressions. Operatg ower Ga, G. From (1) and substitutg (1) and (14): G or 1 1 G ource end oad end (1.8),(17) Available Ga, G A. From () and substitutg (15) and (16): av, n 1 1 G A 1 (1.1),(18) 1 1 av, 11 Transducer Ga, G T. From (3) and substitutg (14) and (15): 1 1 GT 1 (1.13),(19) 1 1 av,

8 Whites, EE 481/581 ecture 33 age 8 of 11 It can also be shown that G T can be expressed as 1 1 GT av, 11 (0) (i) Discussion All of these ga expressions (17)-(0) are formed by the product of three factors. The first and third describe how the power ga is reduced (or accentuated) by the source and load circuits, respectively. (ii) G and G A conta portions of G T. More specifically, the last two terms G are the same as those (19), while the first two terms G A are the same as those (0). (iii) It is apparent from (17) that G is not dependent on Γ (or Z ). From (18) we deduce that G A is not dependent on Γ (or Z ). However, G T is dependent on both Γ and Γ. (iv) If the source and load are both conjugate matched, (i.e., * * and ) then G GT (19) and GA GT (0) such that G G G (1) T A (v) If 0 (i.e., the source and load are matched for zero reflection rather than conjugate matched) then from (19) () GT 1 1

9 Whites, EE 481/581 ecture 33 age 9 of 11 while 1 G 1 and 1 GA. 1 Example N33.1. (imilar to text example 1.1.) The put and put matchg networks shown below are designed to produce and Calculate G, G A, and G T given the followg parameters for the transistor , , Z Z Z Z From (6), From (7),

10 Whites, EE 481/581 ecture 33 age 10 of With these reflection coefficients and the given parameters, we can now compute the requested ga quantities. From (17), 1 1 G 1 1 From (18), G db G A G db A From (19),

11 Whites, EE 481/581 ecture 33 age 11 of G T db Observe that G while GT 9.44 av, av, 9.44 We see from these two equations that av,. Hence, we can deduce that because G GT, then the put power,, is less than the maximum power available from the source, av,. Additionally, with and G G av, n A av, T av, we can deduce that nearly all of the power available from the network is delivered to the load.

Low Noise Microwave amplifiers with improved input matching applicable in active array antennas

Low Noise Microwave amplifiers with improved input matching applicable in active array antennas JAE, VO. 17, NO.1, 15 JOURNA OF AIED EECTROMAGNETIM ow Noise Microwave amplifiers with improved put matchg applicable active array antennas M.. Tonev Technical University of ofia, Bulgaria Faculty of Tlecommunication,