was recommended by Associate Editor David Haigh. D. L. Danyuk is with the Department of Solid-State Electronics. lnstile. of Physics. Ukrainian Academy of ...
912
IEEE TRANSACI10NS CIRCUITS AND SYSTEMS-I: FUNDAMENTAL THEORIES AND APPLICATIONS. VOL. 41. NO. l2. DECEMBER 1992
Feedforward Amplifiers Incorporate Parallel Output Summing Dimitri L. Danyuk and George V. Pilko
Abstract-A practical method of designing a feedforward amplifier which a higher efficiency is obtainable, unlike the known analogs with resistive output summing network. A design example is given.
Index Terms-Circuit theory and design, amplifiers, active network feedforward error correction. I
L INTRODUCI10N
Feedforward error correction is a powerful tool for improving a amplifier distortion and noise figure. An error feedforward amplifier system uses a second signal path to amplify the error signal. The err{)r signal is defined as the difference between the input and the output of the main channel. The output of the auxiliary path is combined with the output signal of the main path so that the error. originated in the main channel. is canceled at the load terminals. This principle was successfully applied to very high frequency (VHF) amplifiers [1]1 it reduce distortion by several orders of magnitude. In the VHF regime directional couplers, three winding transformer and Wheatstone bridges act as sum/difference input/output network [1]. [2]. While these networks combine characteristic impedance matching with low noise and small power loss, the practical cons ide rations when applied to low frequency amplifiers make it necessary to omit them. In this case an output-summing network comprises resistive divider [2]-[4]. otherwise a floating load is required [5].
Manuscript received June 2. 1993; revised December 8. 1993. This paPeR was recommended by Associate Editor David Haigh. D. L. Danyuk is with the Department of Solid-State Electronics. lnstile. of Physics. Ukrainian Academy of Sciences. Kiev 252 028. Ukraine. O. V. Pilko is with the Department of Superconductor Electronics, lnstite of Metal Physics. Ukrainian Academy of Sciences. Kiev 252 134. Ukraine IEEE Log Number 9406628.
1057-7122/94$04.00 © 1994 IEEE
R\ R,
tv\
in
out
,j,.
V;f
.,I".
tvz
R7 -R •
.J,. Fig. I. Basic configuration of a feedforward amplifier with a passive parallel output summing network.
(a)
Rl
Let us consider a resistive output-summing network, shown in Fig. I. The output voltage of the amplifier can be written as Vo
+ V2g2 + g2 + gL
vigi
= gl
R,
(I)
out
and the voltage drop across divider resistors as .,
R•
(2)
V2 - Vo
+ g,(V2 - vd = gl +gLV2 g2 + gL g, + g2 + gL
(3)
II. FEEDFORWARD ERROR CANCELLATION
The basic configuration of the feedforward amplifier with a passive parallel output-summing network is shown in Fig. I. The following definitions apply: Vi is the input signal, G I and G 2 are the gain of amplifier halves, and d l and d2 are their distortion, respectively. The output signals can be written VI + Vz = --_.
2
1
1 + gL/2g 1
=
= 2 + VigL j gl [G I + G z (1 + G 3) -13G , G 2G 3j 1 j [d l +d2 -Jd t G2G3j. +gL gl
Fig. 2. Practical circuits of (a) inverting and (b) noninverting feedforwarct amplifiers.
Under assumption that the amplifier halves are identical (G 1 = G 2 • d l = d 2 , pC I = 1) the distortion tenn in (7) will be canceled when (8
=
If (8) holds, the output signals are VI = ViGt +d l , V2 ViG, - d 1 Distortion components cancel while the signal components reinforce one another and the remaining fundamental tenn can be rewritten as Vo
G, = 1 + gL/2g v,. 1
(9
Fig. 2 shows a schematic of inverting and noninverting amplifier, that use operational amplifiers for amplifying channels. The output voltages (Vb V2, V3) of the amplifier presented in Fig. 2(a) can be written as VI + V2 1 (10 Vo = --2-·- . "-1-+-R=-d""-2-=R:-L
(II
(12
where .13 is the subtractor network attentuation function, and G 3 is the gain of the correction amplifier, gl 1/ RI = 1/ R2. Substituting (5) and (6) into (4), one gets:
+2
Ra
(4)
(5)
Vo
R, •
(b)
where gl = IjR t .g2 = IjR 2 ,gL = l/RL: VI and l'2 are the output signals of amplifying paths. With a view to minimizing the power consumption in R, it should be lower than RL at least by a factor of 3. In order to prevent mutual loading of the amplifying paths, R2 should be chosen much higher than RL. Under such conditions, the required voltage swing from the auxiliary amplifier is so large that the whole system seems inefficient. Alternatively, when the output voltages of amplifier halves are nearly equal (VI ~ V2), the second tenns in the right-hand side of (2) and (3) are small; thus the power consumption in RI and R2 is reduced to a minimum. The system essentially requires a pair of almost identical amplifying paths. Providing that their errors are also equal and controllable, the feedforward principle [5] can be applied to achieve a degree of error cancellation.
Vo
tVo
R.
R~
J.
(7)
IEEE TRANSACTIONS CIRCUITS AND SYSTEMS-I: FUNDAMENTAL THEORIES AND APPLICATIONS. VOL. -II. NO. 12. DECEMBER 1994
914
It is evident from the above analysis that the coefficient of the fundamental term in (13) should be adjusted to obtain nearly equal output voltages in the amplifying paths. and the coefficient of the error term must be zero. Then it is necessary that:3[ = .:32 , A[ = .·h . d 1 d2 , Rs R s /2. ~ Rs/3G, R2 R 3 /(2G + 2) where G = R3/ R[ . Simplifying (13) yields
=
=
Va
--.. -BO.OO (D
Ge d[ = -1 + R 7 /2RL vi + (1 +;3[.4.[)2
a
'-'
Qj
=
=
00000 -
a
'0
> Q)
~ o
.....
(14)
o.AAb.o.
-90.00
0
0
a
-100.00
e=
28[.4[
0
measurement
---------
'- - I I 0.00
+li .4I
(1+;31Ad 2
0
0
a
" floor
"
Q)
where
1
2 - 3
00000 -
L-+---'--t--'--i8,.....--'-----~
10
(15) •
frequency (kHz)
e is the remaining error function of the circuit shown in Fig. 2(a). Let the open loop gain of the operational amplifiers be represented by the one pole model A I (s) ~ ;uti s. The remaining error is given by 1 + 2sr e(sJ= 1+2sr+s 2 r 2 '
Fig. 3. Spectrum of the distortion products produced ' b~ the reference amplifier (I). the amplifier based on Fig. 2(a) (2). and predicted values for the feedforward amplifier (3). (Fundamental frequency 2 kHz. peak·to-peak outpU[ level 10 V.)
(16)
=
where r 1/ p[Wt and w, is the unity gain bandwidth of the operational amplifier. Examining the above error function (16). one can see that the remaining magnitude and phase errors are given by
": == idjw)i- 1 ~ j r~2J } wr . == arg[djw)] ~ -2"," r
~
1.
(17) out
It is clear that relatively negligible magnitude and phase errors are. obtained. It should be pointed out that the dis'tortion is reduced by a factor equal to the square of the return difference 1 +:3 1A.I. that is much oreater as compared with a conventional negative feedback amplifier. Further cancellation can be obtained with phase and time delay compensation. The feedback attenuation
/31
=R
I
R 2 /(R I R 2
+ R1R3 + R2R3)
= .:32 = R4Rs/(RtRs + ~Rs + RsR6) = R I /3(R3 + Rll for the amplifier outlined in Fig. 2(a) is three times lower than for-the amplifier without feedforward error correction. The distortion term in (14) should be lower than the one for the amplifier without error correction. if i3IAI > 3. The performance of the feedforward amplifier can be compared with that of the actively compensated amplifiers employing two operational amplifiers [6). [7]. The above expressions (17) indicate that the magnitude error is a second-order term. whereas the phase error is a third·order term. The residual errors obtained for the compensated amplifier [6). [7] depend upon the loop gain J.) / (31 Wt in the same orders. The majority of the amplifiers based on active compensation belong to an amplifier system with error correction-a structure with active error feedback and input summing. In this topology. the error signal produced by both the error and the main paths is utilized. Detail consideration of various error correction structures is given in (8) . The analysis on the basis of total available gain shows that existing errorcorrection topologies do exhibit the same sensitivity to changes in the main path as does negative feedback. The absence of the regenerative feedback loop and the corresponding overall stability criterion is the main advantage of pure feed forward error correction. The feedforward amplifier shown in Fig. 2(a) was tested for a g!lin of ·8 ,witl) a dual operational amplifier, type 747. The circuit elements have the following values: Rl 2.37 kf2. R2 1.06 kf2. RJ = Rs 19.1 kn. ~ = ,90 f2. R6 = 9.55 kf2. R7 = R~ = ·511 n. RL 5 .11 kn; the unity bandwidth of the operational amplifier J.)t/27r was measured to be 820 kHz; the feedback attentuation :31 is equal to 0 .037. The resistors used were of I % accuracy. The amplifier with two symmetrical signal paths. each being identical with the
=
=
=
=
1110
R, ~ R,o
Fig. 4.
Differential feedforward amplifier circui[ diagram.
a
upper half of the amplifier. shown in Fig .. 2(a). is used as basis for comparison. The 3 dB small-signal bandwidths of reference and feedforward amplifier were measured to be 34 kHz and 82 kHz, respectively. The bandwidth improvement is found to be 2.4; this is in close agreement with theoretical value of 2.483. which can be derived easily from (14HI6). The spectrum of the distortion produced by reference and feedforward amplifiers is presented in Fig. 3. Operational amplifier output stages operate in class A. due to additional 2.2 kD resistors inserted between each amplifier output node and negative supply raiL It is observed that experimental individual harmonic levels differ significantly from the levels. predicted by (14). This is because the two halves of the amplifier have not the exactly equal amount of distortion. The apparent design problem lies in creating antiphase and predictable error components. In particular. the mismatch of the transition region in conventional AB and B output stages in amplifying paths and its temperature dependence place a limit on the switching distortion cancellation. The other limitation is a finite output impedance associated with the output· summing network. The analysis of the noninverting and differential feedforward amplifiers is almost identical to the case of the inverting one, Design considerations for these circuits are listed below. For the noninvertingamplifier [Fig. 2(b)], R6 Rs/2. Rt R s /(3G..;. 3), R2 R3/2G. where G 1 + R3/ R I . For the differential amplifier (Fig.) . R6 . Rs/2. R4 .=;:. R;/3G. R2 (R3 + GR.)/(2G + 2). where G R3/ R 1 , and the highest common mode rejection ratio is obtainable when Ra G R, .
=
=
=
=
=
=
=
=
III.
CONCLUSION
In this article, several circuit configurations which can act as a feedforward amplifier are proposed. An analysis of the feed-
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS-I: FUNDAMENTAL THEORlES AND APPLICATIONS. VOL. 41. NO. 12. DECEMBER 1994
forward amplifier with resistive output-summing network is given. The inverting amplifier, in particular. is considered in detail. and its performance is compared with that of the amplifier without feedforward error correction. It should be noted that the proposed feedforward technique is also acceptable for wide-band amplifiers with transformer input-Qutput networks. ACKNOWLEDGMENT
The authors would like to acknowledge the helpful comments and suggestions made by the reviewers. REFERENCES
[I] H. Seidel. "A microwave feedforward el(periment," Bell Syst. Tech. 1., vol. 50, pp. 2879-2916, Nov. 1971. [2J K. B. Klaasen, R. J. de Kok, and J. C. L. van Peppen, "Signal-errorfeed forward-controlled amplifiers," EleClron. Lett., vol. II, pp. 250-251, June 12, 1975. [31 A. M. Sandman. "Reducing amplifier distortion," Wireless World, vol. 80, pp. 367-371. Oct. 1974. [4J G. Stocchino, "Feedforward amplifier," Wireless World, vol. 84, p. 70, May 1978. [5] D. L. Oanyuk and G. V. Pilko;'''Bridge amplifier with feedforward error correction," Electron. Lett., vol. 28, pp. 1058-1059. 1992; H. Jardon. H. Vazquez, and R. Gomes, "Comment: Bridge amplifier with feedforward error correction," Electron. Lett., vol. 28, pp. 2148-2149, Nov. 5, 1992; D. L. Danyuk and G. V. Pilko, "Reply: Bridge amplifier with feedforward error correction," Electron. Lett., pp. 211 ~2117. [6] A. M. Soliman, "Classification and generation of active compensated non-inverting VCVS building blocks," Int. 1. Circuit Theory Appl., vol. 8. pp. 395-405, Aug. 1980. [7J A. Budak, G. Wullink, and R. Geiger, "Active filters with zero transfer function sensitivity with respect to the time constants of operational amplifiers," IEEE Trans. Circuits Syst., vol. CAS·27, pp. 849-854, Oct. 1980. [8] O. L. Oanyuk and G. V. Pi1ko, "Amplifier topplogies with error correction," fzv. VUZ: Radioelektronika (Radioelectron. and Commun. Syst.), vol. 36, pp. 57-62, Aug. 1993.
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