Designed a microwave amplifier circuit with a required bandwidth of 250MHz at a center frequency of 3.7GHz experiencing 6.5dB gain within Keysight ADS.
3. ELEC 4502 Project 2 Report Rashad Alsaļ¬ar - 101006781
1 Introduction
Microwave ampliļ¬ers are designed to increase the radio frequency power of a high frequency signal
and producing a stable bandwidth while negating the eļ¬ects of noise.
Our microwave ampliļ¬er design will utilize a BFP450 GaAsFET bipolar junction transistor. To
establish this we will encounter multiple design steps. A DC bias network was provided to us with
set capacitor and inductor S2P ļ¬les. The Inļ¬neon BFP450 datasheet [1] provided S-parameter ļ¬les
for set DC bias conditions, i.e. voltage and current driven from a DC supply. A selected DC appli-
cation voltage/current would be chosen for this particular application.
The ļ¬rst stage of the design procedure was to check the deviceās stability characteristics. Inļ¬-
neon provided several S2P ļ¬les characterizing S-parameters for the BFP450 at multiple frequencies
tailored to a selected DC voltage/current [1]. The S-parameters were also determined through ADS
simulations of the BFP450 ampliļ¬er conļ¬guration with no input or output matching networks.
After determining the stability of the device, the design procedure could be tailored towards one
of two methods: maximum available gain (MAG) or maximum stable gain (MSG). Within each
method the conjugate input and output reļ¬ection coeļ¬cients Īā
in and Īā
out can be derived to deter-
mine source and load reļ¬ection coeļ¬cients ĪS and ĪL, respectively.
The establishment of the reļ¬ection coeļ¬cients would provide for impedances and admittances nec-
essary to derive input and output matching networks. An alternative method for matching network
creation is also discussed. Each individual matching network was tuned to allow for maximum power
transfer and minimum return loss, ensuring the conditions of the circuit would meet the design
speciļ¬cations described below:
1.1 Design Speciļ¬cations
The list below displays the substrate properties for the Rogers 4350B material used for the ampliļ¬er
fabrication design:
ā H: substrate height = 62 mil
ā r: dielectric permittivity = 3.66 F/m
ā Āµr: dielectric permeability = 0.999994 H/m
ā Cond: substrate conductivity = 5.96 Ć 107
S/m
ā T: conductor thickness = 35 Āµm
ā tan Ī“: loss tangent = 0.0037
The detailed design speciļ¬cations of the 3.7GHz microwave ampliļ¬er are detailed below:
ā Gain = 6.5dB Ā±0.5dB
ā Bandwidth = 250MHz @ 3.7GHz
ā Input VSWR < 1.2
ā Output VSWR < 1.5
ā Source/Load Impedance = 50ā¦
ā Power Supply = +3V w/ max 100mA
ā PCB Size = 2.5in longĆ 2.0in wide
4. ELEC 4502 Project 2 Report Rashad Alsaļ¬ar - 101006781
2 Design Process
2.1 DC Bias Selection
The goal was to design an ampliļ¬er through its S-parameters to establish stability, design for max-
imum available gain, and create input/output matching networks for the transistor circuit. The
circuit is driven by a DC operating system via DC source. A DC bias point was selected from the
BFP450 Inļ¬neon datasheet [1]. A point was selected for 0.57mA at 3V, due to the maximum DC
voltage supply.
Figure 1: BFP450 DC Bias Characteristics Inļ¬neon Datasheet [1]
2.2 DC Bias Schematic
The DC current and voltage bias were selected based on the characteristics described above. The
maximum DC supply was 3V, and to aim for maximum gain, a diagonal line was drawn and a point
was selected in the middle of the line, approximately 0.57mA base current IB. A collector current IC
was selected as 90mA. The ļ¬gure below displays the used DC bias network used within the circuit:
Figure 2: DC Bias Network established for Ampliļ¬er Circuit
A quarter-wavelength microstrip line of width 6mil is placed beneath each side of the DC bias circuit.
The determination of the length of said microstrips will be discussed within Section 2.6.
5. ELEC 4502 Project 2 Report Rashad Alsaļ¬ar - 101006781
2.3 Device Stability Check
2.3.1 Linvilleās Method
Stability could be determined through two diļ¬erent methods: plotting stability circles via Smith
Charts or using Linvilleās Method. Linvilleās Method can be applied by deriving stability conditions
via S-parameters of the device. The BFP450 webpage [4] provided S-parameters for the device at
speciļ¬c bias conditions. A ļ¬le indicating 3V at IC = 90mA was selected. The following S-parameters
were found below at center frequency, upper and lower bands. Note that although a bandwidth of
250MHz was required, the ļ¬le provided frequency values from a range of 200MHz bandwidth, which
was used for the remaining calculations:
Frequency Band S11 S21 S12 S22
Lower-Band: 3.6GHz 0.7706 128.2ā¦
1.909 29.8ā¦
0.1179 33.9ā¦
0.5747 134.4ā¦
Center Freq: 3.7GHz 0.7732 126.8ā¦
1.85 28.5ā¦
0.12 32.7ā¦
0.5784 133.1ā¦
Upper-Band: 3.8GHz 0.7763 125.5ā¦
1.793 27ā¦
0.1221 31.6ā¦
0.5825 131.8ā¦
Table 1: BFP450 S-Parameters for Center Freq., Upper and Lower Band-Edges
The delta factor ā is determined using the expression below at center frequency and each band-edge.
Sample calculation can be seen within Appendix A.
ā = S11S22 ā S12S21 (1)
The ā factors were computed for each set of S-parameters and are displayed in the table below for
center frequency and each band-edge.
Frequency Band ā
Lower-Band: 3.6GHz 0.66 ā103.7ā¦
Center Freq: 3.7GHz 0.661 ā106.3ā¦
Upper-Band: 3.8GHz 0.663 ā108.8ā¦
Table 2: BFP450 ā for Center Freq., Upper and Lower Band-Edges
The Linville stability K-factor is determined using the expression below. Sample calculation can be
seen within Appendix A.
K =
1 + |ā|2
ā |S11|2
ā |S22|2
2|S12S21|
(2)
The K factors were computed for each set of S-parameters and are displayed in the table below for
center frequency and each band-edge.
Frequency Band K-Factor
Lower-Band: 3.6GHz 1.145
Center Freq: 3.7GHz 1.136
Upper-Band: 3.8GHz 1.137
Table 3: BFP450 K-Factors for Center Freq., Upper and Lower Band-Edges
6. ELEC 4502 Project 2 Report Rashad Alsaļ¬ar - 101006781
2.3.2 Stability Circles
The ideal model of the BFP450 device was designed through a schematic within ADS, and is shown
below. DC bias conditions were put in place for all future measurements.
Figure 3: Ideal BFP450 Schematic w/ DC Bias Conditions
Device stability can also be determined via stability circles. Source and load stability circles can be
plotted within the Smith Chart on ADS, as shown below:
Figure 4: Source and Load Stability Circles for BFP450 Device
The unilateral ļ¬gure of merit U can be calculated to determine if a device is bilateral, i.e. S12 = 0.
If U lies within bounds no less than a few tenths of a dB, the device is characterized as bilateral.
The unilateral ļ¬gure of merit is expressed below. Sample calculation is displayed in Appendix A.
U =
|S12||S21||S11||S22|
(1 ā |S11|2)(1 ā |S22|2)
(3)
7. ELEC 4502 Project 2 Report Rashad Alsaļ¬ar - 101006781
A calculated unilateral ļ¬gure of merit was determined as 0.371. The bounds for U are characterized
by the transducer gain GT and the unilateral transducer gain GTU in the expression below:
1
(1 + U)2
<
GT
GTU
<
1
(1 ā U)2
(4)
The deļ¬ned expression above is calculated within Appendix A. The simpliļ¬ed expression for the
bounded unilateral ļ¬gure of merit assumption at center frequency is displayed below:
0.532 <
GT
GTU
< 2.527 ā ā2.74dB <
GT
GTU
< 4.027dB
2.3.3 Device Stability Conclusions
For a device to have unconditional stability it must have a K-factor greater than 1, and a magnitude
of ā greater than 1. Table 3 displays |ā| less than 1. Table 4 displays K-factors all greater than 1.
These calculated terms conļ¬rm the device is unconditionally stable.
To determine the stable region within within Figure 4, we examine the of S-parameters S11 and
S22. Since magnitudes |S11| < 1 and |S22| < 1, this conļ¬rms that the stable region is located outside
of the source and load stability circles, respectively.
The derivation of the unilateral ļ¬gure of merit allowed us to determine necessary bounds to evaluate
the transducer gain. The range is not within a few tenths of a dB, conļ¬rming that the device is in
fact bilateral. Due to the conclusion of a bilateral network and unconditionally stable device, we can
further evaluate matching networks tailored towards maximum available gain.
2.4 Design for Maximum Available Gain
2.4.1 Source/Load Reļ¬ection Coeļ¬cients
Previously we concluded we had a bilateral network and unconditionally stable device due to the
calculated stability conditions. Maximum available gain can now be established for said device, where
the input and output can be matched simultaneously. The necessary values required for matching
are the source and load reļ¬ection coeļ¬cients, ĪS and ĪL, respectively, detailed by the expressions
below:
ĪS = Īā
in =
B1 Ā± B2
1 ā 4|C1|2
2C1
(5)
ĪL = Īā
out =
B2 Ā± B2
2 ā 4|C2|2
2C2
(6)
The following constants are dependent on the device S-Parameter, characterized by the following
expressions:
B1 = 1 + |S11|2
ā |S22|2
ā |ā|2
(7)
B2 = 1 + |S22|2
ā |S11|2
ā |ā|2
(8)
C1 = S11 ā āSā
22 (9)
C2 = S22 ā āSā
11 (10)
8. ELEC 4502 Project 2 Report Rashad Alsaļ¬ar - 101006781
The table below displays the calculated results for equations 5-10. Values are expressed for solutions
towards a matching network designed towards MAG. ĪS and ĪL can be solved using Ā±, so two results
will be displayed for each. Extended solutions for said equations are displayed within Appendix A.
Variable Result
ĪS(+) 1.353 ā 132.8ā¦
ĪS(ā) 0.739 ā 132.8ā¦
ĪL(+) 3.022 ā 171.2ā¦
ĪL(ā) 0.331 ā 171.2ā¦
B1 0.826
B2 0.3
C1 0.395 132.8ā¦
C2 0.0894 171.2ā¦
Table 4: Matching Condition Variables for Input/Output Networks
Given quadratic expressions from equations 5 and 6, two solutions were determined for ĪS and ĪL.
For the purpose of minimum reļ¬ection and maximum power transfer throughout the device, the
smaller of the two values was selected, i.e. the (-) results for both reļ¬ection coeļ¬cients.
MAG can now be calculated using the expression below. Sample calculations for the following
four expressions will be provided within Appendix A.
MAG = GTMAX = GS Ć GO Ć GL (11)
where each of the additional expressions within GTMAX are deļ¬ned below:
GS =
1
1 ā |ĪS|2
(12)
GO = |S21|2
(13)
GL =
1 ā |ĪL|2
|1 ā S22ĪL|2
(14)
Maximum available gain GTMAX was determined to be 7.04, equivalent to 8.48dB. The necessary
gain according to design speciļ¬cations is 6.5Ā±0.5dB, asserting our calculations thus far to obtain the
necessary gain.
2.4.2 Normalized Source/Load Impedances
The determined reļ¬ection coeļ¬cients for the input/output matching networks can be used to deter-
mine the impedances for said input/output matching networks. The expressions below evaluate the
normalized impedances for the necessary matching networks:
ĖZS =
1 + ĪS
1 ā ĪS
(15)
ĖZL =
1 + ĪL
1 ā ĪL
(16)
9. ELEC 4502 Project 2 Report Rashad Alsaļ¬ar - 101006781
The normalized admittances are computed below to evaluate the source and load impedances and
implement them within the Smith Chart.
ĖYS =
1
ĖZS
(17)
ĖYL =
1
ĖZL
(18)
The table below details the calculated normalized impedances and admittances dedicated towards
the input and output matching networks. Results are expressed in polar and rectangular form. Sam-
ple calculations for equations 15-18 are provided within Appendix A.
Variable Result (Polar) Result (Rectangular)
ĖZS 0.46 ā67.3ā¦
0.18 -j0.42
ĖZL 0.51 ā6.5ā¦
0.51 - j0.06
ĖYS 2.17 67.3ā¦
0.84 + j2.00
ĖYL 1.97 6.5ā¦
1.96 + j0.22
Table 5: Normalized Source & Load Impedances/Admittances
2.4.3 Issues with MAG Design
A glaring issue was encountered when pursuing the development of input and output matching
circuits using MAG Design. When developing matching networks via load and source impedances
and admittances, the goal was to develop matching networks similar to the ļ¬gure below:
Figure 5: Characterized Input/Output Matching Network for Ampliļ¬er Circuit
Realistically, the shunt lengths would have been smaller than the series lengths for both source and
load; unfortunately this was not the case.
When plotting source and load impedances and admittances within a Smith Chart, determined
series lengths were less than half of the determined shunt lengths, disapproving of our original incli-
nations for matching network design.
When developing and simulating the circuit within ADS, the ampliļ¬er gain had reportedly dropped
below -20dB, far from the required design speciļ¬cations. Due to the issues surrounding MAG design
within our circuit, another solution was pursued to further develop successful matching networks.
10. ELEC 4502 Project 2 Report Rashad Alsaļ¬ar - 101006781
2.5 Matching Network Development via Smith Chart
Various Smith Charts were developed and plotted regarding the ideal ampliļ¬er system characterized
in Figure 3. S-parameters S11, S22 and reļ¬ection coeļ¬cients Īin, Īout were measured at the design
frequency of 3.7GHz. In order to assert proper input and output matching networks S11 and S22
were designed as goal impedances for each individual input and output matching networks.
Individual matching circuits were designed with the conjugates of Īin and Īout acting as the TermG
impedances. Mentioned S-parameters acted as the goal load to track from the center 50ā¦ of the
Smith Chart towards said S-parameters. The following table represents the simulated input/output
reļ¬ection coeļ¬cients and S-parameters used within the matching networks:
Parameter Value
Īin 41.8 + j96.85
Īout 26.95 + j5.20
S11 29.55 - j94.00
S22 54.85 - j77.75
Table 6: Ideal BFP450 Īin, Īout, S11, S22
2.5.1 Input Matching Network
The following Smith Chart was designed within RF Buddy Online Smith Chart Tool, using various
series and shunt transmission lines surrounding 50ā¦ towards S11:
Figure 6: Input Matching Network Smith Chart Characterization
Each transmission line was expressed as an ideal TLIN component and tuned to evaluate S11 to-
wards the center of the Smitch Chart. This was followed by the inclusion of MLIN components,
where LineCalc was used to convert impedance and electrical length to microstrip dimensions. Said
MLIN components were tuned once again to meet desired conditions.
An MTEE component was placed between unmatched impedance components, mainly due to the
inclusion an MLOC component; an open-circut shunt stub is easier to design than a short-circuit
shunt stub, and is therefore used in our conļ¬guration. The addition of an MTAPER component
helped fashion unmatched microstrip impedances with minimal spacing required.
11. ELEC 4502 Project 2 Report Rashad Alsaļ¬ar - 101006781
The schematic below details the implemented input matching circuit from the Smith Chart above:
Figure 7: Input Matching Network Schematic
2.5.2 Output Matching Network
The following Smith Chart was designed within RF Buddy Online Smith Chart Tool, using various
series and shunt transmission lines surrounding 50ā¦ towards S22:
Figure 8: Output Matching Network Smith Chart Characterization
The output matching network circuit was designed similarly to the input matching circuit, given the
components used within ADS. The schematic of the output matching circuit is displayed below:
Figure 9: Output Matching Network Schematic
Each established matching network required tuning of their microstrip dimensions to tweak existing
conditions towards a more suitable matching experience. Together the matching networks as well as
the established DC bias circuitry from Figure would connect to BFP450 conļ¬guration, as well as the
DC bias circuitry.
12. ELEC 4502 Project 2 Report Rashad Alsaļ¬ar - 101006781
2.6 Final Microwave Ampliļ¬er Design
Each matching network was created separately and joined together with the functioning BFP450 to
form a complete microwave ampliļ¬er.
Figure 10: Final Microwave Ampliļ¬er Schematic
where X1 identiļ¬es the BFP450 transistor connected to the DC bias network, X2 identiļ¬es as the
input matching network and X3 as the output matching network.
In reference to Section 2.2, the DC bias network was to be connected to both the base of the
transistor and within the input and output matching network simultaneously. To ensure the DC
eļ¬ects of the bias network would have no impact on the transmission line network connected in se-
ries to the BFP450 a quarter-wavelength microstrip was placed at each end of the DC bias network.
Given it must have a width of 6mil, its length required further calculation.
A quarter-wavelength transmission line can be expressed as 0.25Ī», where Ī» can be calculated in
the expression below:
Ī» =
c
f
ā
r
(19)
Descriptive calculation of Ī» can be found within Appendix A. Given a relative dielectric of the used
substrate RO4350B as 3.66 [2], Ī» can be solved as 0.0424m. A quarter wavelength can be expressed
as 0.25 Ć Ī», equivalent to 0.0106m or 417.32mil.
2.7 Ampliļ¬er Measurements
2.7.1 Ampliļ¬er Gain, Return Loss
The plot below displays the ļ¬nal microwave ampliļ¬er gain and return loss, characterized by S-
parameters S21 and S22, respectively:
Figure 11: ADS Simulation of Microwave Ampliļ¬er Gain and Return Loss
13. ELEC 4502 Project 2 Report Rashad Alsaļ¬ar - 101006781
The plot above details the ampliļ¬er gain and return loss at the upper and lower band-edges, as
well as center frequency at 3.7GHz. The gain at center frequency, upper and lower band-edges is
measured to be 7.455dB, 7.483dB and 7.405dB. The ampliļ¬er gain lies within the Ā±0.5dB range from
the given design requirements. As for the ampliļ¬ed gain range beyond 6.5dB as per speciļ¬cations,
a higher gain achievement through basic ADS simulations is appreciated, as in realistic scenarios a
device may not always replicate its simulation counterpart.
Figure 11 above displays ampliļ¬er return loss experiencing a very low value S22 at center frequency,
approximately -38.661dB. A minimum return loss asserts that maximum power transfer will occur
at the deviceās operating frequency. The upper and lower band-edges experienced a return loss of
-25.372dB and -24.625dB, respectively.
2.7.2 Ampliļ¬er Stability
The plot below details the stability measurements of the ampliļ¬er:
Figure 12: ADS Simulation of Microwave Ampliļ¬er Stability Check
Previously in Section 2.3 we calculated device stability using stability circles and Linvilleās Method,
each of which conļ¬rmed that our device was unconditionally stable. The plot above details two
factors, StabFact and StabMeasure, which correspond to the K-factor and |ā|, respectively. Since
K > 1 and |ā| > 0, we can assert the ļ¬nal ampliļ¬er design is unconditionally stable.
2.7.3 Ampliļ¬er VSWR Response
The plot below details the VSWR response of the ampliļ¬er:
Figure 13: ADS Simulation of Microwave Ampliļ¬er VSWR Response
14. ELEC 4502 Project 2 Report Rashad Alsaļ¬ar - 101006781
Input VSWR was recorded at 2.645 while output VSWR was recorded at 1.024. According to design
speciļ¬cations output VSWR remained under 1.5, however input VSWR was greater than 1.2. To
receive an ideal VSWR of 1, the input/output reļ¬ection coeļ¬cient must be nearly 0 to achieve this.
Issues due to an imperfect matching network may explain the deviating input VSWR result.
3 Further Analysis
3.1 BFP450 S-Parameters
The determination of the BFP450 S-parameters was recovered directly from Inļ¬neon [1] ļ¬le base.
In hindsight, the ideal method to determine the S-parameters of the BFP450 at 3.7GHz and appro-
priate DC conditions, simulations should have been utilized to determine said parameters. Using
simulated-produced S-parameter values could have improved the MAG design method. This in turn
would potentially result in superior matching networks for the overall design. Appendix B contains
simulated plots for the BFP450 S-parameters with no matching networks attached.
3.2 DC Bias Components, Transistor
Each component used within the circuit is given an ideal value within ADS. However, when fabri-
cated to a PCB, the values of the used components have a tolerance, i.e. an estimate of component
value ļ¬uctuation depending on the application. This would in turn aļ¬ect the VSWR and gain of the
fabricated circuit, causing deviation from the measured values.
The included capacitors GJM1555C1H6R0CB01D and C0805C104K5RACTU, inductor MLZ2012N220LT000,
and BFP450 transistor do not portray their simulation counterpart. Individually manufactured com-
ponents will have a varied tolerance value aļ¬ecting their impact towards circuit gain and VSWR.
This eļ¬ect explains the diļ¬erences between simulated circuit responses via ADS and measured values.
3.3 Solder and Feed Lines
Solder was used to cement 50ā¦ SMA connectors on the input and output of the fabricated PCB.
The eļ¬ect of using solder could potentially cause a slight phase shift as well as act as a source of loss
due to the solder material not being a perfect conductor. The skin dept within regions of the solder
decrease which correlates with increased conductor loss due to the surface roughness of the material.
This leads to increased return loss, another reason as to why measured and simulated values will diļ¬er.
The addition of input and output feed lines into the SMA connectors would have to connect to
the input and output matching networks. This would cause the ampliļ¬er to experience more loss
due to the lines. Longer microstrip lines experience more loss, justifying our aim to create matching
networks with small microstrip lines.
4 Conclusion
The ampliļ¬er project proved semi-successful in its approach and outcome. Many design procedures
were implemented to optimize the design of the BFP450 ampliļ¬er circuit. Ampliļ¬er traits such as
stability, input/output and source/load reļ¬ection coeļ¬cients, S-parameters, source/load impedances
and admittances, and maximum available gain were purposeful properties that led to the determi-
nation of developing matching networks.
15. ELEC 4502 Project 2 Report Rashad Alsaļ¬ar - 101006781
Although MAG design did not go as planned within our approach another design method operated
by Smith Chart matching was attempted, and input/output matching networks were schematized
and simulated.
Due to issues developing an acceptable layout, a PCB was not fabricated for this project, how-
ever analysis has been determined for an ideal case with working microwave ampliļ¬ers. Due to
damaged transistors while testing, measured results were unable to be determined through the VNA.
Nonetheless, ADS simulations justiļ¬ed the operating nature of the ampliļ¬er at an acceptable gain
with minimum return loss at operating frequency. Input VSWR did not meet the design speciļ¬-
cations, among faults within the matching networks, however future analysis using appropriately
determined S-parameters of the BFP450 may provide further insight towards ļ¬xing existing issues.
5 References
[1]: Inļ¬neon Technologies AG. (n.d.). BFP450. Retrieved from https://www.inļ¬neon.com/cms/en/
product/rf-wireless-control/rf-transistor/high-linearity-si-and-sigec-transistors-for-use-up-to-6-ghz/bfp450/
[2]: Rogers Corporation, RO4350B Laminates. Retrieved from https://www.rogerscorp.com/documents/
726/acs/RO4000-Laminates-RO4003C-and-RO4350BData-Sheet.pdf