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

2 The Effects of Phasing Errors on Sideband Suppression

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

 
cos(($\displaystyle\omega_{c}^{}$ $\displaystyle\pm$ $\displaystyle\omega_{a}^{}$)t) = cos($\displaystyle\omega_{c}^{}$t)cos($\displaystyle\omega_{a}^{}$t) $\displaystyle\mp$ sin($\displaystyle\omega_{c}^{}$t)sin($\displaystyle\omega_{a}^{}$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 j$\scriptstyle\omega_{a}$t to be one audio signal, and VBe j$\scriptstyle\omega_{a}$t to be the other, the result of using a nonideal phasing network will be

 
Re[cos($\displaystyle\omega_{c}^{}$t)VAe j$\scriptstyle\omega_{a}$t + sin($\displaystyle\omega_{c}^{}$t)VBe j$\scriptstyle\omega_{a}$t] = $\displaystyle{\textstyle\frac{1}{2}}$Re[e j($\scriptstyle\omega_{c}$ + $\scriptstyle\omega_{a}$)t(VA - jVB) + e - j($\scriptstyle\omega_{c}$ - $\scriptstyle\omega_{a}$)t(VA + jVB)], (2)

and the sideband suppression (or enhancement) is given by

 
20$\displaystyle\log_{10}^{}$$\displaystyle\left \vert \frac{V_A + j V_B}{V_A - j V_B} \right\vert.$ (3)

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

 
- 20$\displaystyle\log_{10}^{}$|tan($\displaystyle{\frac{\delta}{2}}$)|. (4)


next up previous contents
Next: 3 Analyzing the HA5WH Up: Originally published in August Previous: 1 Introduction