926 



THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1953 



bands of frequencies, one band in the region of four times carrier fre- 

 quency and the other in the video frequency band starting at zero 

 frequency. The lower frequency component of this product is selected 

 by a low pass filter following the product modulator yielding, 



if - Qt) 



Sin 2-i, + PQ Cos 2<i>. 



(8) 



The dc component of the low pass filter output is a suitable control 

 voltage for synchronization and is obtained in the limit as the cut-off 

 frequency of the low pass filter is lowered. Average values as produced 

 by the low pass filters are applied as a frequency control voltage to the 

 carrier oscillator. 

 The first term in equation (8) 



{P' - Q') 



Sin 20 



when averaged is, for small errors in carrier phase angle, proportional 

 to the error angle <t>. The factor of proportionality is recognized as the 

 difference in mean squared values of the ^'real" and quadrature modulat- 

 ing functions, P and Q, illustrated typically in Fig. 5. This difference is 

 always positive when the modulating signal contains energy components 



VESTIGIAL SIDEBAND 

 SIGNAL INPUT 





/ <[' P COS Ct + Q SIN Ct\ l± [P COS + Q SIN 0]\ VIDEO 



i 



'y^ 



CARRIER 

 OSCILLATOR 



|cos(ct-^)|- 



DEMODULATOR 



UOW-PASS 

 FILTER 



POLARIZER 



SIGNAL 

 OUTPUT 



note: BRACKETED EXPRESSIONS 



INDICATE VOLTAGE FUNCTIONS 



EXCEPT FOR CONSTANT 



MULTIPLIERS 



C = 2 77" X CARRIER FREQUENCY 



▼ {^ (P^- Q2) cos 2 Ct + PQ SIN 2 Ct]> 



SQUARER 



BAND -PASS 

 FILTER 



MODULATOR 



45» 

 PHASE 

 SHIFT 



SQUARER 



BAND- PASS 



FILTER 



2fr. 



LOW -PASS 

 NETWORK 



,- {2 (P^~ Q^) SIN 2 0+ PQ COS 24>\ 



H 



SIN (2Ct -2 



0)} 



Fig. 7 — Functional diagram of the L3 homodyne demodulation process. 



