Page 231 - Build Your Own Transistor Radios a Hobbyists Guide to High-Performance and Low-Powered Radio Circuits

1 . - - 1 1
For example,

'- I I 1 I

Also, in general,

1
eX!·1 = 1 + Xl/[ a (1] {X2/[ 2)(2 1 l} + {Xl/[( 3)( )(2 (l)]) + . . . + {xlT/[ n)(n!]}
14-7)
The preceding general equation is rather daunting. But generaHy, we are concerned
only with a few or at most the first four terms of this equation. If more terms are to
be calculated, there are computers to do that!
Now let's use the preceding general equation to figure out what happens when

and

/ . 2

with v in units of volts.
And we will just calculate the first three or four terms:

e 'ig/ ( 02 = + f(v V: + (74 'f v 2 ]Vs~~ + ~ + (14- )
ig :1
By using Equation (14-5),

I =
(
this then leads to the collector current being equal to

le == I . [1 + 38/ v)V ig 740/ v 2 st~ + ,467 /V·i V.~g + .. . ] 4- )

The equation for the collector current shows that there is a squared term and a
cubic term that will (at least) provide distortion of the second and third orders.
From Equation (14-1) on the FET's square-law characteristic, a modulation effect on
two signals occurs with the squared term. Since the bipolar transistor also includes
a squared term, we can expect that the bipolar transistor will generate a

modulation effect with two input signals as well. And this modulation effect is what
we are looking for in a single-bipolar-transistor mixer.
It should be noted that the generalized Equation (14-9) is reallly only valid for peak
sinusoid waveforms of about 26 mV or less. At input signals of 26 mV peak, the