Radio Frequency Integrated Circuit Design - Webs

86 Radio Frequency Integrated Circuit Design
a source resistance of 50�. The matching circuit must have a bandwidth of
200 MHz and the circuit is to operate at 2 GHz.
Solution
The matching circuit will look much like that shown in Figure 4.25. We will
use the secondary of the transformer as a resonant circuit so that there will be
no reactance at 2 GHz. We first add capacitance in parallel with the input
capacitance so that the circuit will have the correct bandwidth: Using (4.30),
C total =
1
R BW =
1
= 7.96 pF
(100�)(2� � 200 MHz)
Note that the secondary ‘‘sees’’ 100� total, due to 200� from the load
and 200� from the source resistance. This means that C extra must be 6.96 pF.
Now, to resonate at 2 GHz, this means that the secondary of the transformer
must have an inductance of
L s =
1
� 2 o C s
1
=
(2� � 2 GHz) 2 = 0.8 nH
(7.96 pF)
Now we must set the inductance ratio to turn 200� into 50�:
L p =
R effR L L s k 2
R 2
L − � 2 o L 2 s (1 − k 2 ) 2
50� �200� �0.8 nH � (0.8)
=
2
(200�) 2 − (2� � 2 GHz) 2 (0.8 nH) 2 (1 − 0.8 2 ) 2
= 0.13 nH
Figure 4.25 Transformer matching network used to match the input of a transistor.