Design and Analysis of a Broadband Microwave Amplifier

Received Sep 8, 2020 Revised Nov 27, 2020 Accepted Dec 17, 2020 This paper presents the procedures involved in the design and analysis of a microstrip broadband microwave amplifier. For system design, simulation, optimization and analysis, a Computer Aided Design (CAD) tool known as Agilent Advanced Design System (ADS) was employed. The amplifier deviceFLC317MG-4 FET, was tested for stability, and was observed to be unconditionally stable between 2 to 6 GHz frequency band. Two possible ideal matching circuits were investigated to identify the best matching circuit with the maximum transducer power gain. It was observed that the quarter-wave transformer with parallel open circuit stub, gave a high gain at a wider range of frequency (larger bandwidth/ broadband), than the other matching circuit. Hence, it was employed for the broadband amplifier design using microstrips, and achieved a maximum flat gain of about 9.8 dB to 10.118 dB, at a bandwidth of 3.5 to 4.5 GHz.

This paper looks at the design of a microstrip broadband amplifier, at a microwave frequency range of 3.5 to 4.5 GHz, using Agilent ADS (Advance Design System).

THEORETICAL BACKGROUND
In amplifier design, it is necessary to ensure maximum gain, stability and minimal losses. All these steps are discussed, and some terms and parameters that are required for a proper understanding of amplifier design process are also discussed.

Gain
This refers to the ratio of the magnitude of the power output to the magnitude of the power input. Three types of amplifier gain definitions exists. They are: • Power Gain (GP): this is the ratio of the power supplied to the load, to the power supplied to the amplifier.
• Available Gain (GA): this is the ratio of the amplifier power output to the available source power. • Transducer Gain (GT): this is the ratio of the power supplied to the load, to the available source power. In amplifier design, the transducer gain is the most important parameter in determining its effectiveness and performance. The transducer gain is given as: Where ГS and ΓL are the source and load reflection coefficient respectively, S11 and S22 are the reflection coefficient at port 1 and 2 respectively, S21 is the forward transfer gain, and S12 is the reverse gain.

Maximum Gain
The maximum (unilateral when S12 = 0) gain is the best possible gain that can be achieved. It is the optimum gain of the amplifier, and can be achieved when the input and output networks of the amplifier are conjugate matched [9] to the transistor, and when the system is stable. It is determined by the S-parameters, i.e when ΓS= S11*, and ΓL= S22*. Maximum Gain is given as [10]: An important factor to consider in amplifier design is the trade-off between the gain and bandwidth. This is shown by the transfer characteristics of an amplifier with lumped coupling elements [11]. Ref. [12] discusses how this trade-off can be avoided, while [13] proposes how the bandwidth accuracy and bandwidth gain-independence can be increased.

Stability Analysis
Device stability is indeed an important factor to consider in amplifier design [14]. This is because an amplifier which is unstable may act as an oscillator, which is undesirable [10]. Hence, it is necessary to investigate if the active device is conditionally stable or unconditionally stable [15,16,17].
An amplifier is unconditionally stable if |ΓS|<1, and |ΓL| <1, for all passive source and load impedances, and conditionally stable only for a certain range of passive source and load impedances [16]. The stability of an amplifier is frequency dependent. An amplifier can be stable at a particular frequency, but unstable at another. A trade-off exists between the stability and bandwidth of an amplifier [18].

Input and Output Matching Circuits
In other to maximize the gain, for maximum power transfer, and to minimize losses due to reflections, matching of both the input and output network is required [9]. In the design of an amplifier, maximum gain can be achieved by tuning the circuit components with the tuning function in ADS, or by matching the input and output circuits using a smith chart.

DESIGN PROCEDURE AND RESULTS
The process of amplifier design includes some important steps, which must be followed carefully, to achieve the desired result. These procedures and key parameters are summarized as follows:

Stability Analysis
In amplifier design, it is necessary as a first step, to investigate the stability of the active device which will be used [10,15]. This is because, it is one of the most important characteristics of an amplifier, (else it becomes an oscillator).
The stability of the device-FLC317MG-4 FET, with a drain source voltage of 10V and drain current of 720 mA, as shown in Figure 1 was tested using ADS.
Other key parameters include: -Frequency Sweep range of 2 GHz -6 GHz and steps of 0.5 GHz.
Load and Source terminals of 50 Ohm each. The circuit was simulated, and the S-parameters, the stability factor (K) and the stability measure (b), of the transistor device was gotten. Results: After simulation of the FET device in Figure 1, the results of the stability analysis was given in Table  1 and Figure 2.

Comments:
A device is assumed to be stable if S11 < 1 and S22 < 1. According to the S parameters, it was observed that the device is stable at the frequency range between 2-6 GHz.
According to the stability analysis, an amplifier is said to be unconditionally stable if the stability measure (b) is greater than zero, and the stability factor (K) is greater than 1. According to the stability measure and stability factor plots shown in Figure 2, the device was observed to be unconditionally stable within the bandwidth of 2-6 GHz.
It was also observed that the forward transfer gain S21 is much greater than S12, which further confirms the stability of the system, and proper matching of the device. Hence, the device is potentially stable at the given frequency range 2-6 GHz, but could be potentially unstable at other frequency ranges.

Ideal Matching Circuit
In other to match the circuit, and get the maximum transducer gain, the values for the Simultaneous Match-Input Impedance (SmZ1) and Simultaneous Match-Output Impedance (SmZ2) were generated at 4GHz (centre frequency) using the SmZ1 and SmZ2 functions in the ADS and given as: SmZ1 = 32.264 -j57.757 Ω, and SmZ2 = 14.160 -j4.85 Ω.
The SmZ1 and SmZ2 give an output value of zero when the device is unstable, and tells us the conjugate matching impedances when the device is unconditionally stable. The values of SmZ1 and SmZ2 at 4GHz were used to determine the best matching network (i.e the network with the highest gain and widest bandwidth) out of two possible matching networks, which are: • Short circuit parallel stub with series transmission line, • Quarter-wave transformer with parallel open circuit stub. Using the Smith Chart, with the values of SmZ1 and SmZ2 generated, the two networks were matched as follows:

Short Circuit Parallel Stub with Series Transmission Line
In the case of the input matching, the source impedance was set to be SmZ1, which was connected in series to the transmission line, and the transmission line was connected to a 50Ω load impedance in parallel with a short circuit parallel stub. The circuit was matched (from source to load) by setting the impedance values of the transmission line and the short circuit stub at 50Ω, and then varying the electrical length (E). The new matched values of the electrical length for the input and output were recorded in Table 2.
For the output matching, the same procedure was performed as the input, but changing the source impedance to SmZ2.

Quarter-wave Transformer with Parallel Open Circuit Stub
For the input matching, the source impedance was set to be SmZ1, which was connected in series to a quarter-wave transformer with a fixed length of 90 o , and then matched to the 50Ω load impedance through a parallel open circuit stub.
For the output matching, the same procedure was performed as the input, but changing the source impedance to SmZ2. The new matched values of the electrical length (E) and impedance (Z) were recorded in Table 3.

Ideal Maximum Transducer Power Gain
After the two circuits have been matched using smith chart, the values of the various impedance and electrical lengths were used to design the two input and output circuit components of the amplifier. The two circuits were simulated, and the Maximum Gain, and S-parameter plots were generated and analysed for both circuits.

Short Circuit Parallel Stub with Series Transmission Line
The amplifier circuit shown in Figure 3 was designed according to the matched circuit parameters given in Table 2.

Results:
The amplifier circuit shown in Figure 3 was simulated, and the maximum gain response and return loss obtained is shown in Figure 4. Comments: From Figure 4, the maximum gain of the amplifier was observed to be 10.564dB, which represents the maximum transfer gain S21, (showing that the circuit is matched) and occurs at frequency of 4GHz. It was also observed that at 4GHz, the return loss was very low. This could imply that at 4GHz, the amplifier would yield maximum amplification with little loss or reflection. It was also observed that the gain is high at a very small range of frequency (i.e narrowband). It was also observed that SmZ1 and SmZ2 had values of about 50Ω at 4GHz, which shows that the input and output circuit is matched.

Quarter-wave Transformer with Parallel Open Circuit Stub
The amplifier circuit in Figure 5 was designed according to the matched circuit parameters given in Table 3.

Results:
The amplifier circuit in Figure 5 was simulated, and the maximum gain response and reflection coeffcient obtained is shown in Figure 6. Comments: From Figure 6, It was shown that the maximum gain of the amplifier is 10.564dB, (in its ideal case) which represents the maximum transfer gain S21, showing that the circuit is matched and occurs at 4GHz. It was also observed that SmZ1 and SmZ2 had values of about 50Ω at 4GHz, which shows that both the input and output circuit is matched. It was also observed that for both matching circuits, we achieved same high gain, but the quarter-wave transformer with parallel open circuit stub, gave a higher gain at a very wide range of frequency (larger bandwidth/ broadband). In other words, the quarter-wave transformer with parallel open circuit stub, gave a flat gain at a wider range of frequency than the short circuit parallel stub with series transmission line. As a result, this was considered to be the best match broadband amplifier circuit, which shall be employed using the microstrip.

Microstrip Broadband Amplifier with Constant Transducer Power Gain
For a more practical design, the MLIN microstrip physical line models are employed to replace the ideal lines. The amplifier specification is a constant 10 +/-0.2dB flat gain, with a bandwidth of 3.5 to 4.5 GHz. Using the gain circle tool under Simulation S_Param palette in the ADS, the locus of reflection coefficients that would yield the maximum gain, was seen on the smith chart, and the conjugate matching impedances required for both the input (and output) matching networks were determined. The gain circle was plotted directly on the smith chart using the GaCir tool (for input impedance matching), setting the frequency sweep from 3.5GHz to 4.5GHz, with a step of 0.5GHz.  Figure 7), the normalised impedance of 1.340-j0.99 was chosen as the SmZ1, since it is closest to the 50Ω point (midpoint). The matching was performed using a smith chart, setting the SmZ1 = 1.340 -j0.99, and leaving the SmZ2 unchanged. After matching, new input matching circuit parameters were obtained and presented in Table 4. These new circuit parameters were employed in the design of the broadband amplifier circuit, and also including microstrip Tees and Steps where necessary. The circuit was simulated and the transducer gain was optimised by tuning, using the tune facility in the ADS. After the gain has been increased, at particular values of the electrical length and impedance, the equivalent values for the length and width of the microstrips are gotten using the Linecalc tool in the ADS. Using these new equivalent values of the line length and width of the microstrip, the Microstrip Broadband Maximum Transducer Power Gain Amplifier was designed as shown in Figure 8. The circuit was simulated, and the maximum gain was plotted. The circuit was tuned at the input to give a flat gain characteristic of about 10dB, across a frequency of 3.5 to 4.5 GHz. The new circuit parameters were recorded in Table 5. The microstrip broadband amplifier circuit in Figure 8 was simulated, and the maximum flat gain response and reflection coeffcient obtained is shown in Figure 9.

Comments
It was observed that the flat gain broadband was achieved between 3.5 to 4.5GHz. The maximum transducer gain specification of 10dB +/-0.2 was also achieved.
It was also observed that due to a wider bandwidth, the gain achieved was smaller. This is as a result of the trade-of between the bandwidth and the gain. That is for a broader bandwidth, the gain has to be reduced. In other words, you cannot have more of the bandwidth without having to give up some of the gain. The bandwidth is inversely proportional to the gain.
An increase in the reflection coefficient (S11) of about -9dB was also observed in the microstrip broadband amplifier. This could be as a result of the losses in real practical conditions of the microstrips, unlike the ideal line components.

Comparison with Existing Designs
Various broadband microwave amplifiers with different topologies and frequency band have been compared. Table 6 shows a summary of the different amplifiers and their performance in comparison with this design. It is observed that this design has a good performance with a high gain at the given frequency band.

CONCLUSION
In this paper, a microstrip broadband microwave amplifier was designed and analysed using Agilent ADS. The design procedures and parameters were presented. In the amplifier design process, the S-parameters, stability factor and stability measure were suitable for investigating the stability of the amplifier, and other properties like the gain and losses.
The microstrip broadband amplifier was achieved within a bandwidth of 3.5 to 4.5 GHz, and a maximum flat gain of around 9.8 to 10.118 dB. The transducer gain was maximized and the reflection coefficient minimized by matching of the input and output circuits using the smith chart and by tuning (using the tune function) of the ADS. There is a trade-off between the bandwidth and gain of the amplifier. As one increases, the other decreases.