Mathcad - ee217projtodonew2.mcd

Ballast Resistor Sizing
The term ballast is of Swedish origin, where bal means " to bear," and llast means "load."
Thus the term ballast means to bear the load. The load refers to a heavy weight placed at the
bottom of ship to stabilize the ship in heavy waves. The term ballast is used here to describe a
resistor, which is added to the circuit to provide stability. Most transistors given by a
manufacturer are only conditionally stable. For this reason, and the reasons described above a
ballast resistor is added to stabilize the transistor
The following procedure is used to find the ballast resistor needed to make the amplifier
unconditionally stable, or to provide the desired K factor. First, the procedure involves
converting a given set of S parameters to ABCD parameters and multiplying them with the S
parameters of a parallel resistor. Then the combination ABCD parameters are converted back
into a new set of S parameters, which are used to find the K factor for the device. The value of
resistance is swept to find the value need to meet a desired value of K factor.
ABCD Parameters of a Parallel Resistor
ABCD( R)
1
ohm
R
0
1
S to ABCD Parameter Calculation
S2ABCD S,
Z 0
Note: The units are removed, for calculation purposes only
1 S .
1, 1
1 S 22 ,
S .
12
.
2S 2,
1
,
S 2,
1
ohm 1 S .
1, 1
1 S 22 ,
S .
.
12
Z .
0
2S 21 ,
,
S 21 ,
Z 0 1 S .
1, 1
1 S 22 ,
S .
.
12
ohm
.
2S 21 ,
1 S .
1, 1
1 S 22 ,
S .
12
.
2S 2,
1
,
S 21 ,
,
S 2,
1
S2ABCD Sparam N, I C , s , 50 ohm
=
0.063 0.013i
1.39. 10 4 1.384i . 10 3
2.099 17.814i
0.013 0.042i
ABCD to S Parameter Calculation
ABCD2S ABCD, Z 0 A ABCD 11 ,
B ABCD 12 ,
C ABCD 21 ,
A
D ABCD 22 ,
1
B . ohm
Z 0
Z 0
C. D
ohm
.
A
B . ohm C. Z 0
D
Z 0 ohm
2
A
2.( A. D BC . )
B . ohm
Z 0
Z 0
C. D
ohm
ABCD2S S2ABCD Sparam N, I C , s , 50 ohm , 50 ohm
=
0.537 0.038i
0.129 4.151i
1 0
KwithR( S,
R) K ABCD2S S2ABCD( S,
50 ohm)
. ohm ,
1
50 ohm
R
0.015 0.098i
0.648 0.278i
K Factor with Load Resistor
KwithR Sparam N , I C , s , 1000 ohm = 1.082