RESISTANCES 



attenuator interposed. The 'attenuation' or 'insertion loss' of the section, in 

 dB's, is 



^out 



but Pin = ^ and Pout = ^* 



r R 



and since generator and load are matched, r = R, then 



Pin _ l^m _ 1 



Pout F^out 02 



.-. Attenuation = 10 logjo (—] = 20 losjo ^ or 20 logio I dB's 



Similarly it can be shown that attenuation in dB's also equals 20 log^o 

 hnl^out- 



Graph 6 may be used to convert a vohage or current ratio, 0, into the 

 equivalent loss in dB's. In using it, the only point to bear in mind is 

 that the two voltages being compared must appear across, or the currents 

 being compared must be flowing through, equal resistances. 



If a number of attenuator sections have voltage ratios 6^, Oo, O3 • • . and 

 they are connected in cascade, the overall transmission factor or voltage ratio 

 is 6^626^ . . . , and the overall attenuation in dB's is 



20 logio 



616062 



but this is equal to 



20 logio } + 20 logio ^ + 20 logio ~ • • • 



X M o 



that is, the attenuation of individual sections is additive. 



We can now say a little more about the stepped attenuator. If only 10 

 or 12 degrees of attenuation are required, perhaps 36 dB's in 12 steps of 

 3 dB's, then types 1 or 2 are quite satisfactory; there is no difficulty in making 

 a 12 way, 3 pole switch. If we wanted up to 100 dB's in 1 dB steps, a single 

 100 way switch would be quite impractical; a much more satisfactory way 

 would be to make a 'decade' attenuator having two knobs, one giving 10 

 steps of 1 dB, and one giving 9 steps of 10 dB's. Decade attenuators would 

 be of type 4. 



Type 3 is called the key-switch attenuator, and uses the property of a 

 sequence such as 1,2, 2, 5, 10, 20, 20, 50 . . . that any number up to a 

 maximum (given by the sum of the sequence as far as it has been taken) may 

 be made by adding together appropriate numbers from the sequence. For 

 example, an attenuator having 6 switches, which control respectively a 1 dB, 

 2 dB, 2 dB, 5 dB, 10 dB and 20 dB section, can produce an attenuation of 

 any whole number of dB's from zero to 40. 



22 



