E F F E C T S OF I N T E R A C T I N G C I R C U I T S ON A P H A S E S H I F T E R

L. P. G e l ' d a n d V. E. Z i n o v ' e v UDC 621.317.772.088

Bridge phase shifters, such as shown in Fig. 1, are used in phase-shift measurements [1] and in checking such devices [2]. In this circuit, the phase shift is controlled by R and is defined by

q~ = 2 arctg oRC, (1)

which applies i f

i + c_t

m T ~

R2 li g �9

Fig. 1

R i = 0 ; R I = ~ ; R l = R ~ , (2)

where Ri is the internal resistance of the signal source and R l is the load resistance.

Under real conditions, (2) can be met 0nly with a certain error, so it is best to know the errors arising from using (1).

One can determine the transfer factor for such a device on the basis of the effects of R i and R /by solving the equations for the equivaIent 4- terminal network [3], which take the following form for Fig. 1:

#2 ~ ei ::0oo

,o 1

6 2i\

, ~ , , 1/71--\

l \ - . - . & I t ' " -4

Fig. 2

~,%,a~R r,

n I ~ ' I " / / \ , , I / \ . ,

, I / \ /~<

90 180

f,*

Fig. 3

Translated from Izmeri te l 'naya Tekhnika, No. 5, pp. 69-70, May, 1975.

�9 19 75 Plenum Publishing Corporation, 22 7 West 17th Street, New York, N. Y. 10011. No part of this publication may be repro- duced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, micro- filming, recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.oo.

749

K

+Ri[

X

where k= 1/wRC; b= R~/R 1.

Then the phase shift is

(1 q-b) (1 - - bk ~" ) b Rk2 q- Rk2 b -]- Rl keb - - Ri - - • -t- 1 -~ b ~ k e R I 1 q- k s b 2

R q- Ri q- R1 b - - Rk 2 b I (R -]- R1 b) (R1 - - Rk 2 b) ] R i R ( l q _ k 2 b ~ ) - ] - '~ l • RR i ( l q_k2b2) - -

{ [ (lq-, b)(R-~-R1 b) 1 - - ]k Ri RRi (1 q-/e ~ b 2) q- - ~ / X

( R @ R l b ) 2 ] 1 R + R b @ R l b - q - R l b ' ( l~ -b )~ } RRI(1 -~-keb e) + Rl l-q-k~b 2 ~- l~_bZk~ ,

(3)

A q - B + F q - D ~ = - - a r c t g , (4)

A i - - B 1 - } - F i @ D i

where

A = R i R l l e ( I ~ - b ) ( R 4 Rib); B = R i k ( R ~ R I b ) 2

F = RRik(R + Rb-t- Rib + Rib'Z); D = RlRRtk (l + b)2;

A i = R ! R R i (1 -~-b) (1 --bk~); B i = RRi b (Rh z qT. R k 2 b q - R i k ~ b - - R 1 ) ;

F x = R i R l ( R q - R i q - R i b - R k 2 b ) ; D l = ( R @ R i b ) X ( R i - - R k ~ b ) Ri.

We consider separately the cases where one of the conditions of (2) is not met and get the following results.

If R 1 ~ ~ ( b ~ 1) and R i ~ 0, Rl ~ *% the error in determining the phase shift is

Similarly, for

and for

h~b = cpb= 1 - - q)b~l = arctg ;~ ( b - - 1)

I q- bk 2

Rz = Re; R i = O; R l ~ oo hepR,l=

--= arctg Rk (Rl~,, 0.5R1) (1 q-k 2) q-Rk'-

R I = R 2 ; R l ~ c ~ ; Ri4=O

Ri R1 le ~f~Ri = - - arctg

R (1 @k 2) ( R I + O , 5 R i ) t R i R i

(53

(6)

(7)

We see from (7) that the following is the initial phase shift when the source has an internal resistance and R=0:

% = - - arc tg (oCR1 R i (8) R~ q- 0.5 Ri

Figures 2 and 3 show the ZX%(r ZXCR i (r and ~ ( r relationships for the ranges in the parameters en- countered in practical circuits. Figure 2 shows the addiuonal phase shifts caused by the load (ZXCR/), the signal source (ZXCRi), and the difference between R 1 and P~(Ar b) as functions of r for 1/wC = 1591.5; the curves are as follows: 1) ZX~0R.; 2) ACRI; 3) A~ b. Figure 3 shows ZX~0Ri and/X~0Rl as functions of ~p for 1/wC =15,915 (the curves

1 are: 1) Aq~Ri; 2) / ',r These curves enable one to define the specifications for linked units in order to provide the necessary accuracy in the phase shift.

L I T E R A T U R E C I T E D

1. V . E . Z inov 'ev et al., Teplofizika Vysokikh Temperatur, No. 5 (1968). 2. G M. Smimov, Izmer i te l ' . Tekh., No. 4 (1970). 3. B.P. Aseev, Phase Relationships in Electronics [in Russian], Zvyaz ' izda t . Moscow (1989).

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