Page 183 - Build Your Own Transistor Radios a Hobbyists Guide to High-Performance and Low-Powered Radio Circuits

And see Table 12-3 for a phase-shifting circuit that holds the gO-degree phase

differential between I and Q channels within ±0.44 degree but over a frequency
ratio of about 25:1 instead of the 10:1, as seen in Table 12-2. For the values shown
in the table, the op amps used may be NE5532 or LM833.
TABLE 12-3 Resistor and Capacitor Values for the Phase-Shifting Circuit that
Maintains a gO-Degree Phase Difference between the I and Q Signal Outputs within
0.44 Degree

Frequency Range Frequency Range Frequency Range
3 kHz to 75 kHz 3.8 kHz to 96 kHz 4.5 kHz to 114 kHz

RiA: 1.62 kn R1A: 1.62 kO R1A: 1.62 kO
RiB: 5.89 kn RiB: 5.90 kO RiB: 5.90 kG
R2A: 14.0 kn R2A: 14.0 kO R2A: 14.0 kO

R2B: 32.4 kf!. R2B: 32.4 kO R2B: 32.4 kG
R3A: 76.8 kO R3A: 76.8 k!1 R3A: 76.8 kf!

R3B: 280 kO R3B: 280 kO R3B: 280 kO
0
ALL capacitors: 500 pF 1% ALL capacitors: 390 pF 1% ALL capacitors: 330 pF 1 /0
A question one may ask is, What is the consequence when the 90-degree
difference in phase between the I and Q channels is off by a degree or two? That

is, if the I and Q channels are 89 or 88 degrees in phase difference, what happens?
It turns out that an image-reject mixer relies on a precise gO-degree phase
differential in order to perfectly cancel out the image signal. An error of a degree or
two causes an imprecise cancellation of the image signal, and thus some of the
image signal will appear at the output of the image-reject mixer.

For a rough approximation, the residual image signal output can be expressed by
the following:

.5

where x is the error phase angle measured in radians. Note that 1 radian = 57.3
degree, so 0.1 radian = 5.73 degrees, and 0.01 radian = 0.573 degree.

For small! values of x measured in radians that are much smaller than 1,
.
1

For example, if x == 0.1 radian, then sinCO.'!) rv 0.1. Again, recall that x is measured
in radians. And for all practical purposes, if x = 0.01, then sinCO.01) = 0 .. 01. And
again, to reiterate, x is measured in radians, and x [in the equation of sin(x) = xfor
small values of x] is notmeasured in degrees.

Also, 1 degree equals 0.0174 radian. So a 1-degree error will result in a residual
image signal of about