INDUCTANCES AND RESISTANCES 



SO for a wide pass-band we need L^, large. The upper turn-over frequency is 

 at 



(Rl + Rs 



{r + R,) 



n' 



C02 = 



L,{1 - k^) 



so for a wide pass-band we need L^ small. Since the requirements for L^ 

 conflict, we drop the notion of the actual turn-over frequencies and consider 

 their ratio, since this gives us a measure of the band-width of the transformer. 



Oiq 



M-, 



(r + R^) + 



Rl + Rs 



n^ 



(1 



k^^^^V + R.) 



n" 



In the special but important case where the generator is matched to the load 



Rs + Rl 



w 



and 



CO, 



CO1 



Rv + r 



4 



1 



k^ 



Summarizing for signal transformers under matching conditions: 



(1) The actual load voltage is «Fout (because our Fout has referred to the 

 primary of the ideal transformer) and in the pass-band this equals 0-5 n Ei^, 

 provided the winding resistances are small. 



(2) The bottom end of the pass-band is at co = (r + Rp)l{2Lj,) 



(3) The pass-band extends over a 4/(1 — k^) fold range of frequencies. 



Danger — saturation 



The equations which have been deduced to describe transformer perfor- 

 mance have been linear, in the sense that it appears that in either pulse or 

 signal transformer the input voltage can be indefinitely increased, to produce 

 a corresponding increase in output voltage. 



Figure 4.38 



For transformers having iron cores this is not so. The Hnear theory assumes 

 the primary inductance L^ to be a constant, and the inductance expression 

 contains the permeabihty of the iron, //, as a factor. If magneto-motive 

 force is plotted against flux produced for a particular core, a curve results 



70 



