5 Optimizing the Sideband Suppression

 The optimum values of R_iC_i can be easily calculated using elliptic functions. Typically, we want the worst case suppression to be the highest possible. This leads us to the equal ripple or Chebychev approximation. The mathematics is straightforward and given in detail by Saraga[3]. For an upper and lower frequency of f_u and f_l respectively, the R_iC_i values for an n section network are,

 

$${\frac{{\rm dn}( \frac{2i-1}{2n} {\rm K}(k),k)}{2 \pi f_l}}$$ (28)

where k = $\sqrt{1-(f_l/f_u)^2}$ , K (k) is the complete elliptic integral of the first kind, and dn (u,k) is a Jacobi elliptic function[4,5].

In the Appendix, I provide a listing of a computer program to calculate the R_iC_i values given the upper and lower frequencies and the n value. In table 1, I give some calculated values for some networks of interest to hams, and their theoretical sideband suppression. These theoretical results will of course be best cases assuming perfect components.

   

f_l f_u n Sup(dB) f₁ f₂ f₃ f₄ f₅ f₆ f₇ f₈

300 3000 4 40.5 332.2 629.8 1429.0 2709.0 - - - -

300 3000 5 52.1 320.5 500.7 948.7 1797.6 2808.1 - - -

300 3000 6 63.7 314.2 435.5 720.3 1249.5 2066.8 2864.5 - -

300 3000 7 75.4 310.4 397.8 595.3 948.7 1511.8 2262.4 2899.4 -

300 3000 8 87.0 308.0 374.0 519.4 771.2 1167.0 1732.7 2406.2 2922.5

200 4000 5 42.9 219.5 398.4 894.4 2008.1 3645.0 - - -

200 4000 6 52.7 213.5 332.1 633.1 1263.6 2408.9 3747.8 - -

200 4000 7 62.5 209.9 294.6 497.5 894.4 1608.2 2715.5 3812.0 -

200 4000 8 72.2 207.5 271.2 417.8 689.9 1159.6 1915.0 2949.6 3854.8

150 6000 6 44.7 163.6 287.7 628.9 1431.1 3128.3 5500.9 - -

150 6000 7 53.1 160.0 247.7 471.0 948.7 1910.7 3633.0 5626.4 -

150 6000 8 61.5 157.6 223.1 381.3 696.7 1291.9 2360.2 4033.2 5710.4

In passing, I note that Saraga's Taylor approximation[3] is given by simply choosing all the R_iC_i values to be the same and equal to ${\frac{1}{2 \pi \sqrt{f_u f_l}}}$ . Also, if maximum suppression is needed at a particular frequency (for example if you wanted to use audio tones in a single-sideband transmitter to produce frequency shift keying), it is simple to select R_iC_i values appropriate for these frequencies, and then optimize the other network sections.