Specifications of Microwave Amplifiers:
Lecture 4: Microwave Amplifiers (1)
Gain (dB): power gain
Component focus: bipolar junction transistors (BJT) and fieldeffect transistors (FET).
Mismatch (or return loss, or VSWR)
The design techniques: employ the full range of concepts of
microwave transmission lines, two-port networks and Smith chart
presentation.
Heavily used S-parameters: The development of S-parameter
matrix concepts grew from the need to characterize active devices
and amplifiers in a form that recognized the need for matched
termination rather than short- or open-circuit termination.
Stability: The amplifiers must not oscillate at any frequencies, for the range of
source and load impedances expected.
Noise figure: how much noise the amplifier adds compared to background noise.
1 dB compression: the input power level where the output power deviates from
linear by 1 dB. Affected by bias point and supply rails. Tied to dynamic range and
power consumption.
2-tone 3rd order intercept point (IP3): When two tones (two close frequencies
ω1 and ω2) are present with equal amplitudes at the input, the output exhibits an
intermodulation product. IP3 is where the extrapolated 3rd order intermodulation
product intersects the extrapolated linear output.
Dynamic range: The difference between the maximum allowable and minimum
detectable input signals.
Microwave amplifiers for our consideration in this lecture:
Small signal so that superposition applies,
Power consumption: DC power consumption
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Modeling of Microwave Transistors and Packages
Third order
intermodulation
output power
IP3
The S parameters of a given microwave transistor can be derived from transistor
equivalent circuit models based on device physics, or they can be measured
directly. Generally, a manufacturer of a device intended for microwave
applications will provide extensive S-parameter data to permit accurate design of
microwave amplifiers. This can be verified by measurement, a step that has
proven important on many occasions.
For a bipolar junction transistor, in addition to intrinsic device parameters such
as base resistance and collector-base capacitance, amplifier performance is
strongly affected by the so-called parasitic elements associated with the device
package, including base-lead and emitter-lead inductance internal to the package.
Similar considerations apply to microwave field-effect transistors.
The magnitude and phase angle of each of the S parameters typically vary with
frequency, and characterization over the complete range of interest is necessary.
Dynamic range of a realistic amplifier
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The S parameters also typically vary with bias. For large-signal applications,
bias-dependent S parameters need to be characterized and modeled.
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Features of interests for RF active devices:
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How do RFICs/MMICs look like?
(1) Maximum power gain bandwidth
(2) Minimum noise figure
(3) Maximum power-added efficiency
(4) Low thermal resistance
(5) High temperature of operation and reliability
(6) Low on-resistance/high off-resistance
(7) High linearity
(8) Low power dissipation
(9) Low leakage current under cut-off operation
(10) Low 1/f noise
(11) Multifunctionality
(12) Low single power supply
(13) Semi-insulating substrate
(14) Mature technology
(15) Low cost
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GaAs MESFET
• Gate barrier is formed by the Schottcky contact between the gate
metal and doped GaAs
• Higher operating frequency are achieved as a result of the higher
electron mobility of GaAs compared to that of Silicon.
An example of component values for a GaAs MESFET
S-parameter characteristics of a GaAs MESFET
2
Cross section of a typical
GaAs MESFET
S 21 > 1
Intrinsic small-signal
equivalent circuit
S12 :
Packaged MESFET model needs to include parasitics, such as
series resistance and inductance at each terminal.
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Unilateral current-gain cutoff frequency, fT
Short-circuit (at output) current
gain under the unilateral condition
is defined as
Gisc =
Id
g V
g
= m c = m
Ig
Ig
ωC gs
fT is defined as the upper frequency limit when the short-circuit
gm
current gain is unity.
fT =
S12 is solely determined by Cgd, which
is usually very small. In this case, the
device is said to be unilateral, and S
12
=0
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• The choice of DC biasing points depends on the application (lownoise, high-gain, high-power), the class of the amplifier (class A,
class B, class AB).
• DC bias voltage must be applied to the gate and drain, without
disturbing the RF signal paths.
• The input and output decoupling capacitors are needed to block DC
from the input and output lines.
2πC gs
DC characteristics
Representing the gain
Biasing and
decoupling
circuit
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Figure of merit:
Physical layout of a MESFET.
The maximum available gain
(MAG)
2
f 
1
MAG =  T 
f
4
R
/
R
+
4
π
f
C
 
ds
T gd ( R + Rg + πf T LS )
Where,
R = Rg + Ri + RS + πfT LS
fT =
gm
2πC gs
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This shows that MAG rolls of by 6 dB/octave. The frequency at
which MAG is unity signifies the maximum frequency of operation
and is given by,
f max = f T [4 R / Rds + 4πf T C gd ( R + Rg + πf T LS )]
−1 / 2
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Si bipolar transistor (BJT)
Current driven
I e = I S [exp( qVbe / kT ) − 1]
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Small-signal equivalent circuit for a microwave
bipolar transistor
q
I ( mA)
∂I
gm = c =
α0 I e = e
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∂Vbe kT
fT
2
f max
=
8πrbCC
fT =
1
2πτ ec
τec: the transit time, or the delay time
from the emitter to collector
Typical component values
fT is given by
fT =
Preferred over GaAs FETs at frequencies
below 2 to 4GHz (may not be true anymore)
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gm
2πCπ
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Heterostructure Field-Effect Transistors (HFETs)
Heterojunction bipolar transistors (HBT)
High electron mobility transistor (HEMT) or Modulated doped
FET (MODFET): for high carrier mobilities and speed
Key advantage: Higher emitter injection efficiency
The doping profile of HBT
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Energy band diagram of HBT
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Two-port network for amplifier analysis
SiGe HBT
Objective: try to derive parameter expressions in terms of the
S-parameter of the network.
Pick your
position!
But be
flexible.
Power Gain G, Available Gain GA, Transducer Gain GT:
PL power delivered to the load
=
G=
Pin power input to the network
Pavout power available from the network
=
GA =
power available from the source
Pavs
PL
power delivered to the load
=
GT =
Pavs power available from the source
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When the input and output are both conjugately matched to the twoport, all the gains are maximized and G = GA = GT .
Definitions of Γ L, Γ s, Γ in and Γ out:
ZL - Zo
ΓL =
ZL + Zo , the reflection coefficient of the load
Zs - Zo
Γs =
Zs + Zo , the reflection coefficient of the source
Zin - Zo
S12S21ΓL
Γin =
= S11+
, the input reflection coefficient
Zin + Zo
1-S22ΓL
Zout - Zo
S12S21Γs
Γout =
=
S
+
, the output reflection coefficient
22
Zout + Zo
1-S11Γs
A typical S-parameter table for a GaAs FET
f GHz
3.0
4.0
5.0
S11
S21
S12
S22
0.80/-89°
0.72/-116°
0.66/-142°
2.86/99°
2.60/76°
2.39/54°
0.03/-56°
0.03/-57°
0.03/-62°
0.76/-41°
0.73/-54°
0.72/-68°
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Power Gain Equations
The equations for the various power gain definitions are
1)
PL
G=P =
2)
GA =
3)
GT =
in
1 - lΓLl 2
1
lS21l2
2
1 - lΓinl
l1 - S22ΓLl 2
Pavout
1 - lΓsl 2
1
=
lS l2
Pavs
l1 - S11Γsl 2 21 1 - lΓoutl2
PL
1 - lΓsl2
1 - lΓLl 2
2
=
lS
l
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Pavs l1 - ΓinΓsl2
l1 - S22ΓLl 2
2
1 - lΓsl
1 - l ΓLl2
2
=
lS
l
21
l1 - S11Γsl2
l1 - ΓoutΓLl2
Read page 606-609 of Pozar for the derivation.
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For a unilateral network, S12=0 and
Γin = S11 if S12=0 (unilateral network)
1)
2)
Model of a single-stage microwave transistor amplifier
Zo
Γout = S22 if S12=0 (unilateral network)
Input
Matching
Circuit
Gs
We can then define the unilateral transducer power gain, GTU,
which is given by
2
2
2
S 21 1 − ΓS 1 − ΓL
GTU =
2
2
1 − S11ΓS 1 − S 22 ΓL
)(
(
)
Output
Matching
Circuit
GL
Transistor
[S]
Go
Γs
Γ in
Γout
Γ
Zo
L
The transducer gain GT can be expressed as the product of
three gain contributions
GT=GsGoGL, where
Go = lS21l 2 ,
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GTU =
G sU =
(
S 21 1 − ΓS
2
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GTU (dB) = Gs (dB) + Go (dB) + GL (dB).
)(1 − Γ )
2
We can maximize Gs and GL by setting Γs = S11* and ΓL = S22* so that
Gsmax =
1
and
1 - lS11l2
GLmax =
1
, so that
1 - lS22l2
L
1 − S11ΓS 1 − S 22 ΓL
2
1 - lΓ s l2
, where the subscript U indicates unilateral gain.
l1 - S 11 Γ s l2
In practice, the difference betw een G T and G TU is often quite sm all, as it
is desirable for devices to be unilateral if possible.
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The components of GTU can also be expressed in decibel form, so that
If the device is unilateral, or sufficiently unilateral so that S 12 is sm all
enough to be ignored, the unilateral transducer gain G TU is sim plified
because
2
1 - lΓsl 2
1 - l ΓLl2
and
G
=
L
l1 - ΓinΓsl2
l1 - S22ΓLl2
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For a unilateral network, S12=0 and
Γin = S11 if S12=0 (unilateral network)
1)
Γout = S22 if S12=0 (unilateral network)
2)
2
Gs =
27
GTUmax =
1
1
lS l2
1 - lS11l2 21 1 - lS22l2
Note that, if lS11l=1 or lS22l=1, GTUmax is infinite. This
raises the question of stability, which will be examined
next.
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These are defined by circles, called stability circles, that delimit lΓinl
= 1 and lΓoutl = 1 on the Smith chart.
Stability
In a two-port network, oscillations are possible if the
magnitude of either the input or output reflection coefficient
is greater than unity, which is equivalent to presenting a
negative resistance at the port. This instability is
characterized by
The radius and center of the output and input stability circles are
derived from the S parameters on (see pg. 613-614 of Pozar).
Output
stability circle
lΓinl > 1 or lΓoutl > 1, which for a unilateral device implies
lS11l > 1 or lS22l > 1.
Thus the requirements for stability are
S12S21ΓL
lΓinl = lS11+
< 1 and
1-S22ΓL l
S12S21Γs
lΓoutl = lS22+
1-S11Γs l < 1
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Input stability
circle
Where,
∆ = S11S22 − S12 S21
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Stable and unstable regions in the ΓL plane
Stable and unstable regions in the ΓS plane
load stability circle
Source stability circle
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Practical microwave transistors: unconditionally stable or
potentially unstable with K < 1 and ∆ < 1 .
Stability Consideration:
Unconditional stable condition:
2
2
In potentially unstable transistors, most of the practical values of K
are such that 0 < K < 1 --- source and load stability circles
intersect the boundary of the Smith chart.
2
1 − S11 − S 22 + ∆
K=
> 1 and
2 S12 S 21
If -1 < K < 0, most region of the Smith chart is unstable. Some
transistor configurations (e.g. some CB configurations) used in
oscillator designs are potentially unstable with negative values of K.
l∆l < 1, where ∆, the determinant of the scattering matrix, is
∆ = S11S22 - S12S21
Conditionally stable: K < 1, operating points for ΓS and ΓL must be
chosen in the stable region, and it is good practice to check the stability
at several frequencies near the design frequency.
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In the potentially unstable situations, the real part of the input and
output impedances can be negative for some source and load
reflection coefficients.
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Example:
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Solutions: conditionally stable at 500 MHz and 1GHz,
unconditionally stable at 2 GHz and 4 GHz.
Input stability circles
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output stability circles
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Resistive loading and negative feedback: improve stability
Even when the selection of ΓL and ΓS produces unstable operation,
the circuit can be made stable if the total input and output loop
resistance is positive
Example: using a resistive loading to stabilize a potentially
unstable transistor
Re( Z s + Z in ) > 0
and
Re( Z L + Z out ) > 0
Adding a resistive load or
adding negative feedback.
Not recommended in narrowband amplifiers because of the resulting
degradation in power gain, noise figure, and VSWRs.
Narrowband amplifier design with potentially unstable transistors is
best done by the proper selection of ΓL and ΓS to ensure stability.
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All four choices of
resistive loading affect the
gain performance of the
amplifier.
In practice, resistive
loading at the input is not
used because it produces a
significant deterioration in
the noise performance of
the amplifier.
Shunt resistor loading at
the output produces the
most acceptable trade-off
between gain and stability
and is most used in
practice.
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