Page 258 - Build Your Own Transistor Radios a Hobbyists Guide to High-Performance and Low-Powered Radio Circuits

2

/: I

where N is the лth harmonic including the fundamental: (N = 1), Т s the duration
i
of the rectangular pulse, апd Р is the period of the pulse.
For а quick verification, let's take а look at а square-wave pulse that has а level at
О volt and 1 volt. The duration of the square-wave pulse is one-half the period for а
50 percent duty cycle. Thus

And

7i'
For the fundamental frequency, N = 1, 50 the coefficient

- - / 2 = 2
'}
1
because the sine of 90 degrees, ог п/2, equals 1. Thi5 2/п factor then 15 In

agreement with the coefficient for the fundamental frequency of а square wave
with levels of О and 1. Also note that the ОС terml ог this square-wave signal from О
to 1 is 1/2 = ОС; thus the square-wave signal SQ( tJ has the following ОС term and
coefficients:

DC а 1 а 2 аз а 4 a s а 6 а 7 аз a g

1 2 О - 2 О 2 О - 2 О 2
- - - - - -
2 11" 311" 5'1Т 7'ТГ 97Т

t = .1 +1 (2'П .t _...L (1 11" l _....L 14'П [) .
2 'iТ 7 ...
15-5)
7i
1
Thus, sampling the input signal S(t) = Ь cos (2пljпt) with S(J t) results in

t Х 21itf t) - ...L 1Т t+-.l...
:\11' S1Т
1i ,l) . . .]

For а quadrature pulse signal QF{t), used in а Tayloe detector, which is а 25
percent duty-cycle pulse (from О to 1) that results in

/

the ОС term, andthe coefficien,ts