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# 2 The Effects of Phasing Errors on Sideband Suppression

The phasing method generates a single sideband signal, given mathematically as cos(( )t) , where the + (-) sign gives the upper (lower) sideband, and = 2fc where fc is the carrier frequency. Similarly, = 2fa where fa is the audio modulating frequency. The cosine can be written as

 cos(( )t) = cos(t)cos(t) sin(t)sin(t), (1)

the basic equation of the phasing method. The multiplications on the right-hand side are accomplished using balanced modulators, and the two audio frequencies (as well as the two radio frequencies) must be 90 o out of phase and of equal amplitude. I will assume that the radio frequencies are exactly 90 o out of phase, and of equal amplitude. Using the usual complex notation with VAe jt to be one audio signal, and VBe jt to be the other, the result of using a nonideal phasing network will be

 Re[cos(t)VAe jt + sin(t)VBe jt] = Re[e j( + )t(VA - jVB) + e - j( - )t(VA + jVB)], (2)

and the sideband suppression (or enhancement) is given by

 20 (3)

Notice if |VA| equals |VB| , that is if the two signals have equal amplitude then for a phase error of , the suppression in dB is simply,

 - 20|tan()|. (4)

Next: 3 Analyzing the HA5WH Up: Originally published in August Previous: 1 Introduction