Single-Stage Amplifiers Simulation for Microwave Applications Using S-Parameters

ABSTRACT A single-stage amplifier circuits containing transistor as BJT or FET transistor were designed for the microwave application using S-parameters, and developed as a lumped circuit then converted to its equivalent microstrip distributed circuits on different substrates such as Alumina (r=9.8) and Beryllia (r=6.3). The output results as power gain Gp, noise figure NF, and stability factor K were obtained. These results were compared with other published worked included circuits having the same conditions. The comparison shows that in case of the feedback applied to the circuit the Gp achieved about (~1.5) dB for BJT circuits along (0.6-1) GHz and noise figure increased about double, where for FET circuit the increasing in Gp about (7) dB along (2) GHz, and noise figure was less than BJT circuit. The physical characteristics are discussed with respect to substrate and show that the substrate with high permittivity was helpful to reach the higher operating frequency and good power gain values.


INTRODUCTION
The development of microwave solid state circuits is directly dependent upon the availability of suitable active devices. Active devices are required as gain blocks in circuit application and to allow a circuit to increase RF energy at a desired frequency. At low frequency, a lumped component used with transistors and diodes as needed, that is, R, L, and C. When the components become about λ/8 long, about 500 MHz to 1 GHz, we may add transmission line components in addition to lumped components. When the free-space wavelength becomes less than 1mm, the designers are usually forced to use distributed transmission line elements where possible. Other forms of transmission are also used due to the limitations of TEM transmission lines, such as waveguides, surface modes, slotline, coplanar waveguide, inverted microstripline, and suspended microstripline (Vendelin et al., 2005). For microwave circuit applications the microwave bipolar transistor BJT, and FET are the two most important and commonly used active elements. The easer method for amplifier circuit design must be guided by a device's measured scattering parameters (S-parameters) to determine the circuit-element values needed to surround an active device or devices in an amplifier design. S-parameters are based upon the concept of incident (a i ) and exiting (b i ) waves in the amplifier circuit. Recently, the cascade and cascaded circuit topologies were implied to achieve higher gain and low noise-figure. The feedback in the microwave amplifier circuits showed that the applying of the negative feedback caused an increase in bandwidth but with degradation in gain. (Abdul et al., 2020). A single stage amplifier achieved high gain and low noise due to the noise optimization used inductive drain feedback, (Othman et al., 2013). Simulation of single stage LNA was performed especially for multi-standard wireless system with two different frequencies using combines of a notch filter with inductive degenerated, (Azman et al., 2015). The most important part of the design relies upon extensive use of RF/microwave software programs. Such as general simulator/optimizer Microwave Office (Abrie, 2009), (Ivan, 2002). In this work, an FET and BJT devices were designed and simulated for microwave applications using S-parameters. Characteristics such as the gain and noise figure were determined for each design. Each model has been compared with previous practical examples published with the same conditions.

Structure and Design Characteristics 1.
At microwave frequency, however voltage and currents have little meaning and amplitudes are better way to describe microwave fields. In the network shown in Fig. 1, (a) and (b) represents the wave amplitude of the incident wave and the resultant wave, (Fuller, 1990). Suppose port 1 as the input and port 2 as output of the network. If the two ports are terminated in their characteristic impedance (Z o ) the physical meaning of scattering parameter can be explained as,  = b/a . So from equation (1), we can write the S-parameters as: S 12 S 11 =b 1 /a 1 , is the input reflection coefficient, for a 2 =0 S 12 =b 1 /a 2 , is reveres transfer coefficient, for a 1 =0 S 21 =b 2 /a 1 , is the forward transfer coefficient. and, S 22 =b 2 /a 2 , is the output reflection coefficient, for a 1 =0 2. When designing an amplifier, many characteristics should be considered such as: Power Gain (G p ): The ratio of the power delivered to the load, to the actual power supplied into a circuit is fined as the G p and given by (Weber, 2001)

Stability (K):
A stability amplifier condition is where there are no unwanted oscillations anywhere, [Davis and Agarwal, 2001]. This condition lead to the following requirement, (Bahl, and Bahartia, 1988); When simultaneously matching a two-port, the maximum transducer gain G max is, (Trinogga et al., 1991) here, if K >1, the sign is usually (-negative sign). The maximum stable gain (G max ), is obtained by substituting K=1 then: These parameters are described in this work and calculated independently by (Microwave Office). Software.

Amplifier Design
Using S-parameters usually completes microwave amplifier designs, since this is the most accurate two-port description of the transistor. The S-parameters of microwave transistor can be measured by using network analyzer system. At any frequency, every designer have to ensure that the input and output matching networks for the amplifiers are matched to 50 ohms load at the input and output terminal [Pozar,2000], and has the following parameters: S 11 , S 22 , and S 21 , with significant magnitude general topology of the single-stage amplifier consists of three stages: the input matching circuit (M1), the amplifier itself and the output matching circuit (M2) (Jung-Jang et al., 2001), (Lu et al., 2010); i. an input lossless matching network M1, ii. an output lossless matching network M2. If the stability factor K>1, the above two networks can be found to give the maximum available gain given expressed by eq. (5). If the stability factors K =< unity, the amplifier could be terminated in matching structure which causes oscillation, that is G a is infinite (Vendelin, 1982). Thus, the stabile design will require some input and output mismatch impractical. There are at least two treatments, (i) adding resistive matching element or, (ii) adding feedback to make K >=1. The design of single-stage amplifier would usually have the following specification, which must be calculated: Gain, (G) flatness(1.5) dB, bandwidth (f 2 -f 1 ), and center frequency (f o ), noise figure (NF). Usually, short-circuit stubs are placed near the transistor to allow dc biasing. The following steps can be tabulating for the design of a one-stage amplifier: i.
Select transistor based upon S-parameters, noise figure and linear output power.

ii.
Calculate K and G a or G max versus frequency. iii. For K >1, select the topologies that match the input and output at the upper band edge f 2 . This will give G max , and S 11  S 22  0 , ideally, for the initial design. Next, the topology may be varied to flatten gain versus frequency at the expense of S 11 and S 22 . iv. After finding initial M1 and M2, make adjustments in topology until the specifications for gain, VSWR are satisfied. v. Design dc bias circuit. Lay out the elements of the complete circuit and check realizably.

Distribution Circuit:
Microwave circuit techniques included printed circuit board (PCB) MIC, and MMIC technologies. The circuit designer uses packaged devices roughly are centimeter in size for PCB circuit (Weber, 2001). Microwave circuit commits of several passive components called resistor, capacitors, and inductors. Then elements are placed in space of substrate. Transmission lines are composed of these elements, but they are distributed over origin rather than being identified with a point in space. In addition to their components, controlled current and voltage sources are used to describe the performance of active elements such as transistor. The substrate is assumed to be perfect conductor and have constant potential everywhere on it. Transmission lines are used to model distributed parameter circuits and its elements such as capacitors and inductors (Weber, 2001). After choosing the values and elements of the designed circuit, it is suitable to do optimization on the results of output the circuit and reaching to the best results. Next, the design will be converted into distributed circuit, so the resistances are converted to its values as a microstrip line with dimensions W, L which equal; (Bahl, 1979  The effective primitively evaluate from eq. (10) if, w/h1, or from eq. (11) if, w/h  1, (Emad, 1991):  Where; L is in nH, and the unit (mils 1/39 mm). The capacitor formed by the metal strip over the ground plane is given by: Where; C in farads,  o =8.86×10 -12 (F/cm) is the permittivity of free space, and  r is the dielectric constant of the substrate. A "fringe factor" q, is included to account for necessary fringing (estimated to be here 10%).

5.
Circuit Material: Any microstrip circuit or structure is made of two parts. The dielectric substrate and metallic conductor on the substrate's face, (Gardiol, 1988). i. The dielectric material of the microstrip is chosen with a homogeneous distribution for its high h, dielectric constant has to be, (2< r <12). And the tangent losses (tan) must be very small (<0.001).
ii. Microstrip metallic deposited on the semiconductor substrate. The metal layers must exhibit the following characteristics: low resistivity (small ohmic losses), sufficient thickness, at least three times the skin depth, the layer must be quite thin (t~0.001mm) and may also be used to realize resistors.
On synthetic substrates all good conductors such as gold, copper, silver, and aluminum are adequate and present a good adhesion. Gold is often selected for the outer layer, due to its very good resistance to oxidation and aging.

6.
Analyzing the Circuit The circuit must be analyzed to display the output results and shown by graphs. First the stabilization must be optimized so; i. If the stability graph shows the stability factor K to be less than 1, typically it is necessary to add input and output networks to the transistor device to stabilize it over an extended frequency range.
ii. It will be necessary to edit the element parameter values as we construct the output stability network.
iii. All microstrip elements must have a substrate parameter element in the schematic. iv. The next step is to finish the output stability network. Place and edit elements in the schematic to look like the Fig. (3).
The work is supported by "Microwave Office 2000" package, which is a completely new suite of RF/microwave design tools. The entire design solution is constructed using advanced objectoriented programming methods that result in impressive performance, reliability and ease of use. Microwave Office 2000 was developed by "Applied Wave Research Inc." to provide the user interface for setting up circuits for linear, non-linear, EM analysis, and physical layout.

RESULTS AND DISCUSSION
The results were obtained by using the following procedures: a) Specifying the operating frequency rang that we can find S 11 or S 22 in the lowest value. In our work we have depended on (S 11 ) the input reflection coefficient with units (dB). b) The stability factor must be equal or larger than unity, (k  1) at this range.

c)
Measuring of the value (S 21 ) or power gain with units (dB) at the lumped design working area which we could find S 11 , the lowest value and the litter which is next to it. So, the reflection of the signal does not appear and must not change the gain or S 21 more than (3dB) from the lowest frequency to the highest frequency limits of signal operating area. d) After that it has computed transforming lumped circuit into distributed circuit with changing the elements, like the resistance and some parts of transmission line into form of microstrip line. At the same time the program showed that the output layout for the general figure for microstrip circuit. e) After that the power gain can be measured and it is named here (gain) with units (dB) in this distributed circuit to distinguish on the previous lumped circuit. f) Measuring the noise, if it founds in the form of noise figure (NF) with units (dB), although we are using (LNA) but sometime the transistor showed some noise. In order to reach to the best values, it is depending on the ability of optimize circuit, which is founded by the software (Microwave office) which is used.

BJT Circuit:
This design is for single-stage BJT. It is a simple amplifier using the transistor (A010011), which is working as signal amplification. Alumina substrate was used with dielectric constant ( r =9.8) of thickness h=1mm. The feedback was arranged with fewer models surrounding the transistor of the previous design. The matching was indicated at (0.56GHz) as in Fig. (4).   5) for S-parameters also shows that circuit could work safely up to (1GHz). S-parameters also shows that S 21 increased up to (~13.6dB) at (1GHz) and it is denoted more than that at 0.6 GHz. Fig. (6) shows the gain of distributed circuit was (13.7dB). This G p was about (3.3dB) less than the G max that possible to obtain. The stability of this amplifier is shown in the   (Table 1) and compared with those given reference Rohde, which has the same conditions, (Rohde, 2000). The lumped circuit for Rohde and distributed circuits for this work are shown in Fig. (9) and (10).  In this work the design gives the gain and S 21 about (1.3dB) and (1.7dB) respectively more than ref. design, for both lumped and distributed circuits. We expect that an improvement is due to the feedback, which added some voltage that reduced the expected voltage distortion in this circuit. These increased the input current to the transistor so the output level increased, and may be a phase shift occurs as the output signal adding by feedback. In addition this substrate has thermal conductivity (0.37W/cm.K) which is in middle level but for low frequency it was caused a noise occurs much more than previous reference circuit.

FET Circuit:
A FET type (HMC5008A) was used on the dielectric substrata Beryllia ( r =6.3) with thickness h=1.5mm. The results were compared as in the (Table 2) with those achieved from Anvari, which has the same conditions, (Anvari et al., 1986).
The Fig. (11) for Smith's chart shows matching of this circuit arrived at the frequency 7.5GHz.  Fig. (12) gives the high value of S 21 (15.4dB) at the lowest value for S 11 in the frequency 7.5GHz too. This value is fixed along 2GHz frequency width, where far of this range. We expect reflection amplitude was observed as the level of S 11 rises. The gain of distributed circuit was (15.5dB) as shown in Fig. (13). This value fixed and extended along operating frequency between (6.0-8) GHz. Here we pointed the power gain (P G ) coincide with maximum gain (G max ) level. But the stability factor was observed higher, more than one as shown in Fig. (14). The noise figure (NF) was equal to 3 dB as in the Fig. (15), but it indicated (1.5dB) only in the reference.  In this design a short transmission line with a feedback on transistor has been successfully used for input and output matching network and to increase the linear gain. This achievement gives a good result (~7dB) in both gain and S 21 values. But this design appears a double value of noise Fig. (3dB), along operating frequency range of 2GHz. By using Beryllia (BeO) with permittivity (6.3) lower than alumina (9.8) the increasing of power gain at higher frequency was caused a noise figure increased, at high frequency. (BeO) presents a very large thermal conductivity that makes its use particularly interesting for high power applications. The design shows little shift in operating frequency this may be due to the discontinuity for new added microstrip components of this circuit. The results obtained from the modified circuits are tabulated in (Table 3). The linear power gain of BJT with high permittivity was good as well as for FETs. The noise figure of FETs is lower than BJTs. The stability was more than one for both circuits. The substrate materials, which have high permittivity and low thermal conductivity, remove the produced heat slowly and noise figure may rise in BJTs more than FETs. Here it is possible to say that BJT and FET amplifiers could be improved by using: (1) The feedback concept such as the lossless-feedback which may be used in BJT or FET amplifier design. This could be arranged surrounding the transistor. In some way the feedback acts as a directional coupler that can increase the output signal with respect to input signal. If there is no out of phase one could get a lower noise figure with higher linear gain. (2) The substrate and its dielectric losses which have an important role in the performance of the designed circuit such as: (i) BJT circuits with substrate of high permittivity, work at low frequency up to 1GHz and output gain could be high, but this may lead to increase noise figure value. Thermal conductivity has little effects here. (ii) FET circuits the high permittivity substrate was work at higher frequency and output gain could be high also, but in this case the noise figure value lower than BJT. It was found that the operating frequency was more than of BJT.

CONCLUSIONS
In this work we have used special known substrate and transistor. The acceptable circuits produced the optimized results for the linear power gain, noise figure, and stability factor. Both the BJT and FET were used in the designed circuits, with same dielectric substrate. The package software helped to find the accepted and the best circuits that give good output results as power gain, the noise figure and stability factor. From the results we conclude: i.
The BJT circuits using substrate with high permittivity ( r =9.8), were worked at low frequency up to 1GHz, and the operating frequency was narrow. The output gain found to be within (~13.6), the noise figure was high up to ~5dB. ii.
In FET circuits using substrate of permittivity ( r =6.3), the operating frequency worked up to 7.5GHz. The power gain obtained was within (15.5dB). The noise figure was relatively less than BJT.
iii. The feedback concept has an important role also in this work. It acts as a directional coupler and increases amplitude of the output signal with respect to input signal. The magnification due to this feedback may raise the noise figure as the linear gain increases.