Cathode-Drift Compensation in D-C Amplifiers

J. W . R I T T E N H O U S E M E M B E R A I E E

» Τ Π Η Ε P H E N O M E N O N of c a t h o d e drift r ep resen t s o n e X of t h e m o r e t r o u b l e s o m e sources of drift in d i r ec t -

c o u p l e d ampli f iers , a n d a l t h o u g h t h e exac t m e c h a n i s m s involved h a v e n o t b e e n c o m p l e t e l y e x p l a i n e d , it is gene ra l l y a c c e p t e d t h a t t h e cond i t i ons of drift c a n b e s i m u l a t e d , for ana ly t i ca l pu rposes , b y t h e a s s u m p t i o n of a r a n d o m noise-vol tage g e n e r a t o r in series w i t h t h e c a t h o d e of t h e t u b e in ques t ion .

S u c h a n a s s u m p t i o n p rov ides t h e basis in this a r t i c le for t h e analysis of t h e Mi l l e r C i r cu i t w h i c h seems to h a v e a n excel lent abiUty t o c o m p e n s a t e for t h e effects of c a t h o d e drift, b u t w h i c h has h a d associa ted w i t h it t h e l im i t i ng cond i t ion t h a t t h e ampl i f ie r l oad res i s tance , in F i g u r e 1, m u s t b e l a rge e n o u g h to m a k e t h e ampl i f ie r p l a t e c u r ­r e n t , / i , smal l c o m p a r e d to ΐ2> T h e p u r p o s e of this a r t i c le is to d e m o n s t r a t e t h a t s u c h a l im i t a t i on does n o t exist a n d to p ropose a v a r i a t i o n of t h e M i l l e r C i r cu i t w h i c h h a s some a d v a n t a g e s in m a n y app l i ca t i ons .

T h e a-c e q u i v a l e n t c i rcu i t for t h e Mi l l e r C i r cu i t w i t h t h e gr id of Γ ι g r o u n d e d , is s h o w n in F i g u r e 2 w h e r e r i , μ ι , Γ2, a n d μ2 a r e respec t ive ly t h e p l a t e res is tances a n d a m p l i ­fication factors of T\ a n d Γ2.

A n analys is of F i g u r e 1 revea l s t h a t w i t h t h e g r id of Ti g r o u n d e d :

a n d

(1)

(2)

U s i n g e q u a t i o n 1 to s u m t h e vo l t age a r o u n d t h e t o p l oop of F i g u r e 2, t h e fol lowing express ion is o b t a i n e d :

21 [ ( m i - f -1 ) (/?! + I ? L + ^·2(μι + 1 ) (Λι + / ? 2 ) = (iu 1 + 1 (3)

ό ό Ebb2 Ebb I

Figure 1. The Miller Circuit showing the equivalent cathode

noise-voltage generator, c„

W W

βη Λ Λ Λ Λ - Α Λ Λ Λ

W W

Figure 2. A-c equivalent circuit for Miller Circuit showing the equivalent cathode noise-voltage generator e^

A s imi la r s u m m a t i o n a r o u n d t h e b o t t o m loop of F i g u r e 2 , yields t h e fol lowing exp re s s ion :

i l [ ( M 2 + L ) / ? l + / ? 2 ] + l 2 [ ( / X 2 + L ) / ? l + / ? 2 + r 2 ] = ( M 2 + L>N (4)

S i m u l t a n e o u s so lu t ion of e q u a t i o n s 3 a n d 4 for ii a n d e q u a t i n g dii/de^ t o z e r o yie lds as a c r i t e r ion for c a t h o d e -drift c o m p e n s a t i o n :

gm2 (5)

w h e r e gm2 is t h e t r a n s c o n d u c t a n c e of T2. T h i s resu l t is i den t i ca l t o t h e o n e o b t a i n e d b y Mi l l e r ,

b u t n o a s s u m p t i o n w h a t s o e v e r , r e g a r d i n g t h e re la t ive m a g n i t u d e s of res i s tances o r c u r r e n t s , is m a d e h e r e ; so it w o u l d a p p e a r t h a t th is c i rcu i t shou ld p r o v i d e c o m p e n s a ­t ion w h e t h e r R^, F i g u r e 1, is l a rg e or smal l .

If t h e resistor, Ri, in F i g u r e 1 is shor t - c i r cu i t ed a n d a load resistor is i n t r o d u c e d i n t o t h e p l a t e l e a d of T2, t h e noise vo l tages t h a t o the rwi se w o u l d d e v e l o p in Ri, a n d u n d e r g o ampl i f i ca t ion b y t h e t u b e , c a n b e e l i m i n a t e d w i t h l i t t le sacrifice in ca thode -d r i f t c o m p e n s a t i o n p r o v i d e d t h a t in t h e n e w c i rcu i t t h e r e m a i n i n g c a t h o d e resistor , R2, is m a d e e q u a l t o {l/gm2 + ^ l2 /m2) w h e r e R^z, gm2 a n d μ2 a r e r e spec t i ve ly : p l a t e l oad resis tor , t r a n s c o n d u c t a n c e , a n d ampl i f i ca t ion factor for T2.

Since t h e foregoing findings h a v e b e e n e x p e r i m e n t a l l y con f i rmed , it is be l i eved t h a t th is discussion wil l se rve to b r o a d e n t h e p o t e n t i a l field of a p p l i c a t i o n of t h e o r ig ina l M i l l e r C i r cu i t b y r e m o v i n g a n u n n e c e s s a r y Hmi ta t ion . I t is fu r the r be l i eved t h a t a p p r e c i a b l e benefi t m a y b e de r ived from t h e a d d i t i o n a l possibil i t ies t h a t a r e a v a i l a b l e t h r o u g h t h e p r o p o s e d modi f i ca t ion of Mi l l e r ' s c i rcu i t .

Digest of paper 52-244, "Cathode-Drift Compensation in D-C Amplifiers," recom­mended by the AIEE Committee on Electronics and approved by the AIEE Technical Program Committee for presentation at the AIEE Pacific General Meeting, Phn*inix, Ariz., August 19-22, 1952. Not scheduled for publication in AIEE Transactions.

J . W. Rittenhouse is with the University of Missouri, Rolla, Mo.

A P R I L 1953 Rittenhouse—Cathode-Drift Compensation 299