Radio Frequency Integrated Circuit Design - Webs

176 Radio Frequency Integrated Circuit Design
ic = k 1vs + k 2v 2 s + k 3v 3 s + ...= 0.04vs + 0.8v 2 s + 10.667v 3 s + ...
The dc, fundamental, second harmonic, and intermodulation components
are found in Table 6.1, and equations for them are listed for the above coefficients
in Table 6.2.
The intercept point is at a voltage of 70.7 mV at the input, 2.828 mA
at the output, as shown in Table 6.2 and in Figure 6.26, which agrees with
(6.86). For an input of 70.7 mV, the actual output fundamental current is
11.3 mA, which illustrates the gain expansion for an exponential nonlinearity.
The voltage-versus-current transfer function is shown in Figure 6.27. Also
shown are the time domain input and output waveforms demonstrating the
expansion offered by the exponential nonlinearity.
This diagram illustrates a number of points about nonlinearity.
Due to the second-order term k 2, there is a dc shift. Using the dc component
term shown in Table 6.2, we make the following calculations.
Table 6.1
Harmonic Components
Component With A 1 , A 2 With A 1 = A 2 = A
dc 1m + 0.8A 2
k o + k 2 A 2
k o + k 2
2 (A 2 1 + A 2 Fundamental
2 )
0.4A + 24A 3
k 1 A 1 + k 3 A 1�3 4 A 2 1 + 3
2 A 2 2� k 1 A + 9
4 k 3 A 3
Second Harmonic 0.4A 2
k 2 A 2 1
k 2 A
2
2
2
Intermod 8A 3
3
4 k 3 A 2 1 A 2
3
4 k 3 A 3
Table 6.2
Values for Harmonic Components
A 1 (mV) A 2 (mV) IM3 2nd Harmonic Fundamental Ideal Fund
0.1 0.1 8 pA 4 nA 4 � A 4 � A
1 1 8 nA 400 nA 40 � A 40 � A
10 10 8 � A 40 � A 424 � A 400 � A
20 20 64 � A 160 � A 992 � A 800 � A
30 30 216 � A 360 � A 1.848 mA 1.2 mA
70.7 70.7 2.828 mA 2 mA 11.309 mA 2.828 mA