RESISTANCES AND CAPACITANCES 

 (1 -\-joiCR) — IjoiCR _ 1 (1 —joiCR) 



2(1 +j(oCR) 



BC 



in 



2 (1 +ja)CR) 



1 ( I + (mCRW '^ _ 1 



2 (1 + ((oCi?)2j ~2 



i.e. constant and independent of frequency. Rationalizing 

 V 



B-C 



(1 -jmCR){\ -jcoCR) 1 - (coCRf - IjcoCR 



1^ ~ 1 + {oyCRf ~ 1 + {coCRf 



—IcoCR 

 ''• *^ ^ 1 + ((oCRf 



Remembering the trigonometrical half-angle formulae, 



<f> 



tan 



(joCR 



Thus (f) can have any value between and 180 degrees, for any given co, as 

 CR goes from to oo. 

 A more generally useful version of this circuit is shown in Figure 3.45. It 



Vooi=*Vll 



Figure 3.45 



requires two inputs, equal and in anti-phase, such as may be obtained from 

 a 'concertina' phase-splitter valve, to be described later in this part. The 

 modulus of the output is Kat all frequencies, and the phase shift is tan~^ wCR, 

 referred to the phase of generator 2. 



We now come to consider a group of three, rather more elaborate, R-C 

 networks; they are filters. One will pass all frequencies within a 'band', 

 and attenuate those outside it — a 'band-pass' filter. The other two pass all 

 frequencies except a band, which they attenuate; within the attenuation 

 band there is a centre frequency at which the attenuation is infinite, and the 

 networks are hence known as 'null-transmission networks'. These are the 

 Wien bridge and the parallel T network. 



The R-C band-pass filter 



This is shown in Figure 3.46. When presented with a new and complicated 

 network it is a good plan not to plunge at once into calculations, but rather 

 to get some idea what the network is likely to do. This is achieved by con- 

 sidering what happens when a> is very low, when m is very high, and when to 

 is intermediate. 



46 



