230 



CHARACTERISTIC VALUES FOR THE BILINEAR M CURVE 



Figure 4. Characteristic values for the first mode. 



hand, for positive s, the attenuation constant 

 approaches a finite asymptotic value. It is interesting 

 to note that this is always definitely less than the 

 value s 2 x standard, which corresponds to a single 

 straight line of slope s 2 x standard slope. 



It is also useful to know the real part B of the 

 characteristic value. Figure 4 shows the complex D 

 plane. For g = the Y curve is just standard, and 

 as g increases the value of D for each value of s 

 traces out a curve; for small values of g all these 

 curves practically coincide. For negative s the real 

 part decreases steadily as soon as the imaginary 

 part becomes very small. For positive s, on the other 

 hand, the real part as well as the imaginary approaches 

 a finite limiting value, so that each curve has am 

 end point. 



Some of the consequences of this behavior of the 

 real part can be seen by studying Figure 5. The first 

 row of diagrams shows the situation for fixed nega- 

 tive s and increasing value of g. The first diagram 

 shows the standard curve. The next shows a curve 

 with a small superstandard section, but — B still lies 

 in nearly the same location relative to the dotted 

 line which marks where the origin lay for the stand- 



ard curve; thus B has increased. The first figure of 

 the second line shows how the same thing happens 

 for a small substandard section. Thus for small g 

 the first order effect is just to add the amount g to 

 D, for all values of s. 



In the third diagram of the first row we have a 

 case in which the superstandard has a pronounced 



"B "B O 



n 



-B 



0-B ° _B 



Figure 5. Curves for negative and positive s. 



