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1 of 17
Amplifier Design Tutorial
Introduction
This tutorial will set out the design stages required to design a theoretical microwave amplifier
with the following specification shown in Table 1:
Table 1 Required Specification
Parameter Units
Frequency 1.45 – 1.55 GHz
Gain
12.5 ± 0.2
dB
Noise Figure
≤ 2.0
dB
Output VSWR
≤ 1:1.5 (>13dB)
Gain ripple < 1.5 dB
The first stage in the design process is to pick a suitable device. For X-Band and above GaAs
MESFETS are used while at lower frequencies Bipolar devices are used if noise is not so
critical. Try to pick a device design for the range of frequencies you require. Don’t for example
use an X-band device for an LNA at UHF – you are bound to run into stability problems. Also
pick a device that will give you plenty of gain margin to allow for noise mismatching etc.
For this design an Agilent AT41435 Bipolar transistor has been used. This device has > 14dB
of gain at 2GHz with an associated noise figure of <1.7dB.
To double-check the gain available we can use a simple ‘rule-of-thumb’ estimate by
evaluating
|S21|/|S12|.
At 1.5GHz this will be 4.63/0.063 = 73.5 or 10*LOG(73.5) = 18.6dB
We should easily meet the specification for overall gain and allow for significant output
mismatch to allow for gain equalisation and minimum noise. This estimation needs to be
checked against the stability factor K of the device as this effects the gain and gives an
indication to whether the device is likely to oscillate or not.
The device at 1.5GHz is unconditionally stable with a K of >1.
The ADS simulation shown in Figure 1 has been setup to calculate K factor and plot
minimum noise figure.
Sheet
2 of 17
StabFact
StabFact1
StabFact1=stab_fact(S)
StabFact
Term
Term2
Z=50 Ohm
Num=2
sp_hp_AT-41435_1_19921201
SNP1
Noise Frequency="{0.10 - 4.00} GHz"
Frequency="{0.10 - 6.00} GHz"
Bias="Bjt: Vce=8V Ic=10mA"
S_Param
SP1
CalcNoise=yes
Step=
Stop=2.0 GHz
Start=1.0 GHz
S-PARAMETERS
Term
Term1
Z=50 Ohm
Num=1
Figure 1 ADS simulation to calculate K and minimum noise figure. The resistor-
capacitor combination connected between the gate and source are to ensure that the
device is unconditionally stable at 1.5GHz.
m1
freq=1.526GHz
nf(2)=1.589
1.0
1.2 1.4
1.6 1.8 2.0
1.2
1.4
1.6
1.8
2.0
freq, GHz
nf(2)
m1
freq
1.000GHz
1.053GHz
1.105GHz
1.158GHz
1.211GHz
1.263GHz
1.316GHz
1.368GHz
1.421GHz
1.474GHz
1.526GHz
1.579GHz
1.632GHz
1.684GHz
1.737GHz
1.789GHz
1.842GHz
1.895GHz
1.947GHz
StabFact1
0.944
0.950
0.958
0.968
0.980
0.995
1.012
1.032
1.056
1.083
1.097
1.097
1.098
1.100
1.104
1.110
1.116
1.124
1.134
Figure 2 Results from the simulation shown in Figure 1, showing a K factor >= 1 at
1.4GHz and a minimum noise figure of 1.65dB at our highest frequency of 1.6GHz.
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3 of 17
General Amplifier Design Procedure
Now that we have picked our device, stabilised it and checked it’s maximum available gain we
can begin the process of designing the LNA. This process consists of the following steps:-
(1) Evaluate the Rollett’s stability factor to identify the possibility of instabilities depending on
source and load matching.
(2) Determine Bias conditions and circuit.
(3) If a specified gain is required at a single frequency then the gain circles can be plotted on
a Smith chart and the associated source match can be read off and the corresponding load
match calculated. Careful consideration must be taken to the position of the source match in
relation to the stability circles.
(4) If a specified noise figure and gain at a frequency is required then the noise circles need to
be added to the gain circles from (ii). The source match required will be the intersection of the
required gain & noise circles. Again careful consideration must be given to the position of the
source match in relation to the stability circles.
(5) Once the required source impedance has been chosen the corresponding output match
required for best return loss can be calculated.
Gain & Noise Parameters
Using the S-parameters of the device it is possible to calculate the overall transducer gain
which consists of three parts, the gain factor of the input (source) matching network, the
active device and the output (load) matching network:-
2
22
L
2
o
2
11
s
Los10
2
22
2
L
2
o
2
2
s
S1
1
G
21G
S1
1
G
-:following the to simplified be can
equations above the device) stable a (and 0 = S12 wherecase unilateral the For
)G.G.G(10LOG = gain Transducer Overall
.1
1
G
21G
.1
1
G
−
=
=
−
=
Γ−
Γ−
=
=
ΓΓ−
Γ−
=
S
S
S
L
s
sin
s
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4 of 17
For rough estimate of the maximum gain available we can assume that S12 = 0 therefore at
1.5GHz (Assuming a bias of 8V @ 10mA) the estimated gain is:-
1.14dB = 1.29 =
0.48-1
1
=
S1
1
G
13.31dB =21.43 = 4.63 = S =G
0.68dB = 1.17 =
0.38-1
1
=
S1
1
G
22
22
L
22
21o
22
11
s
−
=
−
=
Total available gain = 0.68 + 13.31 + 1.14 = 15.13dB
Constant Gain circles
G.D1
G.S.S+G.S.S2K-1
p circle gain of Radius
G.D1
*G.C
=r circle gain of Location
S
dB) in not ie (absolute desired Gain
= G = Gain
*SSC
SD
2
2
2
21122112
o
2
2
o
2
21
11222
22
222
+
=
+
∆−=
∆−=
Note the 0dB gain circle will always pass through the centre of the Smith chart.
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