Wide band AC modulated control networks

A twin T network adapted to be connected between a source of AC modulated carrier input signal and a controlled output for the compensation of modulation on said signal wherein the network comprises:

• first and second input terminals and first and second output terminals;
• resistors R.sub.3 R.sub.1, connected in series and comprising the top portion of a first T, and capacitor C.sub.2 connected by one lead from the series connection of resistors R.sub.3 and R.sub.1 to said second output terminal and comprising the vertical portion of said first T;
• capacitors C.sub.3 and C.sub.1 connected in series and comprising the top portion of a second T, and a resistor R.sub.2 connected from the series connection of said last-named capacitors to said second output terminal and comprising the vertical portions of said second T;
• connection means interconnecting the otherwise free terminals of resistor R.sub.3 and capacitor C.sub.3 together;
• first circuit means for interconnecting said otherwise free terminals of resistor R.sub.3 and capacitor C.sub.3 to said first output terminal;
• second circuit means interconnecting said second input terminal and said second output terminal;
• third circuit means for interconnecting the otherwise free terminal of capacitor C.sub.1 and resistor R.sub.1 together and to said first output terminal;
• one of said first and second circuit means comprising a resistor r.sub.1 ;
• a resistor r.sub.2 connected across said output terminals;
• said first impedance transfer function being that of the network comprising:
• first and second input terminals and first and second output terminals,
• first circuit means for directly interconnecting said second input terminal and said second output terminal,
• a series first network comprising a resistor r.sub.1 and a capacitor C.sub.1 in series between said first input terminal and said first output terminal, and
• a second network comprising a resistor r.sub.2 connected across said first and second output terminals;
• said first impedance transfer function T(s) is ##EQU40## and is equal to ##EQU41## where a.sub.1 =r.sub.2 C.sub.1 and b.sub.1 =(r.sub.1 +r.sub.2)C.sub.1 ;
• said impedance circuit having a second transfer function wherein the relationship between said first and second transfer functions is expressed by a frequency transformation ##EQU42## where W is the frequency variable 2.pi.f of said first transfer function and W.sub.1 is the frequency variable 2.pi.f.sub.1 of said second transfer function;
• said second impedance transfer function being determined by said frequency transformation to be T(s.sub.1) is ##EQU43## and is equal to ##EQU44## where ##EQU45## and ##EQU46## is equal to ##EQU47## R.sub.2 is greater than ##EQU48## where D.sub.1 is equal to ##EQU49## and R.sub.2 is equal to ##EQU50## from specifying values for r.sub.1, r.sub.2, R.sub.1 and R.sub.3, where ##EQU51## is made greater than D.sub.2, ##EQU52## is greater than ##EQU53## and D.sub.2 is equal to ##EQU54## C.sub.3 is made equal to ##EQU55## where ##EQU56## where ##EQU57## and C.sub.2 is made equal to ##EQU58## and wherein the carrier frequency is the normalized frequency, w.sub.c =1;
• S is the Laplace complex variable operator;
• b.sub.1 satisfies 0<b.sub.1 <0.5;
• W is representative of the frequency of modulation;
• W.sub.1 is representative of the modulated carrier frequency;
• and
• m is a positive integer in the range of 1 to infinity;
• whereby said network displays an arithmetical symmetry around the carrier frequency, being an even symmetry as to gain response for a bandwidth less than, but substantially equal to, twice the carrier frequency and whereby said impedance network accomplishes a wide band AC modulated effect which affects the modulation of the modulated carrier in substantially the same way as would a network having a said first impedance transfer function and adapted to operate directly on the modulation signal alone.