15-35 15 technical notes and articles copyright 1997-2002 rf micro devices, inc. the nbb and nda-series matched amplifiers may be cascaded in a driver chain or used adjacent to other components such as mixers, oscillators, or filters. in all such in stances, it is desirable to prov ide isolation betwe en adjacent compo- nents to minimize ripple due to any impedance mismatch. "pi" and "t" network attenuators (also known as pad attenu- ators) are simple networks to insert between an amplifier chain (see figure 1) or between an amplifier and adjacent component to minimize ripple over frequency. the following example illustrates a circuit technique to analyze th e "pi" network configuration. 2-stage driver amplifier chain v d in c block rfmd nbb-300 l choke r bias v cc1 c block r 1 r 2 c block r 3 "pi" attenuator rfmd nbb-300 v d l choke r bias v cc2 c block out figure 1. two-stage driver amplifier chain using two nbb-300 amplifiers, along with a "pi" buffer network, used to minimize ripple in the amplifier chain's response. the "pi" network is symmetric and consists of two resistor values, r1 and r2. r 2 37 ? r 1 150 ? r 3 150 ? example 1. s-parameters for a 6db pi-pad attenuator. derive the four s-parameters from the 6db pi-pad attenuator shown. design of ?pi? and ?t? network atte nuators for inter-stage buffering AN0015 AN0015 design of ?pi? and ?t? network attenuators for inter-stage buffering 15
15-36 AN0015 15 technical notes and articles copyright 1997-2002 rf micro devices, inc. solution: notice the "pi" attenuator shown above is a symmetrical circuit, and therefore the knowledge learned from one port may be applied to the other port. (i) s 11 : where and is called the normalized input impedance. solving for z in : calculating in : now s 11 may be expressed in db: (matched in a 50 ? system) (ii) s 21 : where: therefore, s 21 may be expressed in dbs: r 2 37 ? r 1 150 ? r 3 150 ? z in z l 50 ? s 11 ? in z l z o 1 ? 1 + ----------- - === z in z o -------- = z in r 1 r 2 r 3 r l || () + () 49.78 ? = || = in 0.996 1 ? 0.996 1 + ---------------------- 0.00203 == s 11 20 log in () 53 db ? = = r 2 3 7 ? r 1 150 ? r 3 150 ? z in z l =z 0 z s =z 0 v l v 1 v s s 21 2 v l v s ------ - = v l v s ------ - v l v 1 ------ - v 1 v s ------ r 3 z l || r 3 z l || () r 2 + ------------------------------------ - ?? ?? ?? z in z in z s + -------------------- ?? ?? ?? 37.5 37.5 37 + ---------------------- 49.78 49.78 50 + ------------------------- 1 4 -- - = = = s 21 20 log 2 v l v s ------ - ?? ?? ?? 20 log 1 2 -- - ?? ?? 6 db ? ===
15-37 AN0015 15 technical notes and articles copyright 1997-2002 rf micro devices, inc. (iii) s 12 : from symmetry arguments: (iv) s 22 : from symmetry arguments: (matched in a 50 ? system). generally speaking the same arguments and techniques apply to a ?t? configured network. the general representation of each network is shown in figure 2. the values for a 50 ? matched ?t? attenuator network are given in table 1. the complete values for a 50 ? matched ?pi? attenuator network are given in table 2. the attenuation value (s 21 ) usually determines which ne twork is more realistic to construct. s 12 s 21 6 db ? == s 22 s 11 53 db ? == "pi" attenuator r p r s r p r s r p r s "t" attenuator figure 2. general representation of ?pi? and ?t? network with parallel (rp) and series (rs) resistors.
15-38 AN0015 15 technical notes and articles copyright 1997-2002 rf micro devices, inc. table 1. tabular summary of values for ?t? attenuator matched in a 50 ? system t pad attenuator values r s ( ? )r p ( ? )s 21 (db) r in ( ? ) 2 624.0 -0.7 50 4 310.5 -1.4 50 6 205.3 -2.1 50 8 152.3 -2.8 50 10 120.0 -3.5 50 12 98.2 -4.3 50 14 82.3 -5.0 50 16 70.1 -5.8 50 18 60.4 -6.5 50 20 52.5 -7.4 50 22 45.8 -8.2 50 24 40.1 -9.1 50 26 35.1 -10.0 50 28 30.6 -11.0 50 30 26.7 12.0 50 32 23.1 -13.2 50 34 19.8 -14.4 50 36 16.7 -15.8 50 38 13.9 -17.3 50 40 11.3 -19.1 50 42 8.8 -21.2 50 44 6.4 -23.9 50 46 4.2 -27.6 50 48 2.0 -33.8 50
15-39 AN0015 15 technical notes and articles copyright 1997-2002 rf micro devices, inc. table 2. tabular summary of series and parallel values required to construct a ?pi? attenuator matched to a 50 ? system . pi pad attenuator values r p ( ? )r s ( ? )s 21 (db) r in ( ? )r p ( ? )r s ( ? )s 21 (db) r in ( ? ) 60 272.73 -20.83 50 530 9.52 -1.64 50 70 145.83 -15.56 50 540 9.34 -1.61 50 80 102.56 -12.74 50 550 9.17 -1.58 50 90 80.36 -10.88 50 560 9.00 -1.56 50 100 66.67 -9.54 50 570 8.84 -1.53 50 110 57.29 -8.52 50 580 8.69 -1.50 50 120 50.42 -7.71 50 590 8.54 -1.48 50 130 45.14 -7.04 50 600 8.39 1.45 50 140 40.94 -6.49 50 610 8.25 -1.43 50 150 37.50 -6.02 50 620 8.12 -1.40 50 160 34.63 -5.62 50 630 7.99 -1.38 50 170 32.20 -5.26 50 640 7.86 -1.36 50 180 30.10 -4.96 50 650 7.74 -1.34 50 190 28.27 -4.68 50 660 7.62 -1.32 50 200 26.67 -4.44 50 670 7.50 -1.30 50 210 25.24 -4.22 50 680 7.39 -1.28 50 220 23.97 -4.02 50 690 7.28 -1.26 50 230 22.82 -3.84 50 700 7.18 -1.24 50 240 21.78 -3.67 50 710 7.08 -1.23 50 250 20.83 -3.52 50 720 6.98 -1.21 50 260 19.97 -3.38 50 730 6.88 -1.19 50 270 19.18 -3.25 50 740 6.79 -1.18 50 280 18.45 -3.14 50 750 6.70 -1.16 50 290 17.77 -3.03 50 760 6.61 -1.14 50 300 17.14 -2.92 50 770 6.52 -1.13 50 310 16.56 -2.83 50 780 6.44 -1.12 50 320 16.02 -2.74 50 790 6.35 -1.10 50 330 15.51 -2.65 50 800 6.27 -1.09 50 340 15.03 -2.57 50 810 6.20 -1.07 50 350 14.58 -2.50 50 820 6.12 -1.06 50 360 14.16 -2.43 50 830 6.05 -1.05 50 370 13.76 -2.36 50 840 5.97 -1.04 50 380 13.39 -2.30 50 850 5.90 -1.02 50 390 13.03 -2.24 50 860 5.83 -1.01 50 400 12.70 -2.18 50 870 5.77 -1.00 50 410 12.38 -2.13 50 880 5.70 -0.99 50 420 12.08 -2.08 50 890 5.64 -0.98 50 430 11.79 -2.03 50 900 5.57 -0.97 50 440 11.51 -1.98 50 910 5.51 -0.96 50 450 11.25 -1.94 50 920 5.45 -0.95 50 460 11.00 -1.90 50 930 5.39 -0.93 50 470 10.76 -1.86 50 940 5.33 -0.92 50 480 10.53 -1.82 50 950 5.28 -0.92 50 490 10.31 -1.78 50 960 5.22 -0.91 50 500 10.10 -1.74 50 970 5.17 -0.90 50 510 9.90 -1.71 50 980 5.12 -0.89 50 520 9.71 -1.68 50 990 5.06 -0.88 50
15-40 AN0015 15 technical notes and articles copyright 1997-2002 rf micro devices, inc.
|
