This paper portrays the implementation of Linear, Bilateral maximum gain amplifier which is designed for maximum transducer gain in higher frequency applications. This amplifier is designed using Bfp450 RF transistor, which is known for its performance mainly by low-noise figure and high gain [4]. The design was selected to achieve maximum amplification in the frequency range of 2.5 GHz. A systematic approach towards detailed S-parameter analysis and impedance matching was employed to ensure optimal gain performance. Experimental results demonstrated a gain of 7.018 dB, which aligned closely with theoretical predictions. This paper also discusses the stability and linearity of the amplifier [6], making it suitable for various RF applications, such as ‘transmitter’. This design methodology and experimental outcomes provide valuable insights for engineers and researchers aiming to enhance RF amplifier performance.
Keywords— amplifier, S-parameters, maximum gain amplifier, stability, smith chart, Linear Time Invariant Systems, RF and Microwave design.
I. INTRODUCTION
In the rapidly evolving field of wireless communication, the demand for high-performance radio frequency (RF) amplifiers continues to grow. Amplifiers are critical components in Microwave systems, amplifying weak signals to levels suitable for further processing while maintaining low noise and strict linearity. Among the various RF transistors available, the Bfp450 stands out due to its superior gain, low noise figure, and reliable performance across a wide frequency range [4].
** This paper shows the design and working of maximum gain amplifier at the desired frequency of 2.5 GHz. The Bfp450 is a Silicon Germanium (SiGe) bipolar transistor with high cutoff frequency and low parasitic elements, making it an ideal transistor for desired application of this experiment [4]. The amplifier is designed to operate at a collector current of 40 mA.**
** The amplifier was constructed on a Rogers RO4003c substrate, known for its high frequency characteristics. The substrate has a thickness of 32 mil, with a copper cladding thickness of 17µm [5]. As a result, a gain of 7.018 dB was observed with outstanding linearity and stability.**
** The amplifier was designed using AWR Microwave Office and produces in the laboratory of Hochschule Bremen, under the guidance of Prof. Sören Peik. The results of this research highlight the suitability of Bfp450 transistor for high-frequency amplifier applications. The paper further provides a detailed description of the design methodology, including use of simulation tools, substrate selection, and experimental validation. These findings contribute ongoing development of RF amplifiers for upcoming wireless communication systems.**
II. THEORETICAL DESIGN
A. S-parameter
S-parameters (scattering parameters) is main concept in analysis and design of RF and Microwave circuits. S-parameters describe how high-frequency signals respond when encountered by discontinuities in a network, such as reflection and transmission at ports. They help to characterize the network’s behavior based on measurable quantities like reflection coefficient which is a function of frequency. Unlike other parameters such as z-parameters, y-parameters, s-parameters can be directly measure at microwave frequencies without the need of open and shorts circuit conditions, which is difficult to achieve at very high frequencies. This makes s-parameters essential in the design of amplifier where they guide the impedance matching for maximum gain, minimize reflections and ensure stability over desired frequency [1].
** For the transistor Bfp450 with the bias point defined by Vce = 2.00 and Ic = 40.00 at the design frequency of 2.50 GHz, we derive the scattering parameters from the data sheet.**
S11 = -0.620727 + 0.428211j (0.754 ∠145.3°)
S21 = 1.801976 + 1.892261j (2.612 ∠46.39°)
S12 = 0.065872 + 0.059103j (0.088 ∠41.89°)
S22 = -0.478365 + 0.249021j (0.539 ∠152.5°)
B. Reflection Coefficient
The reflection coefficient is a parameter used to describe how much of a wave is reflected by an impedance discontinuity in a transmission medium [2].
B.1. Bilateral Case
In case of bilateral transistor, Γ_in is affected by Γ_out.
Therefore, for maximum gain;
Γ_S^*=S_11+ (S_12 S_12 Γ_L)/(1- S_22 Γ_L ) (1)
Γ_L^*= S_22+ (S_12 S_12 Γ_S)/(1- S_11 Γ_S ) (2)
So Γ_S and Γ_L can be calculated as follows;
Γ_S = (B_1±√(B_1^2-4|C_1 |^2 ))/(2C_1 ) (3)
Γ_L = (B_2±√(B_2^2-4|C_2 |^2 ))/(2C_2 ) (4)
Where B1, B2, C1, C2 are defined as,
B_1=1+|〖S_11 | 〗^2-|〖S_22 | 〗^2-|〖∆| 〗^2 (5)
B_1=1+|〖S_11 | 〗^2-|〖S_22 | 〗^2-|〖∆| 〗^2 (6)
C_(1 )= S_11-∆S_22^ (7)*
C_(2 )= S_22-∆S_11^ (8)*
Equations 3 and 4, along with the scattering parameters mentioned, define the values of input and output reflection coefficients as below.
Γ_S = 1.323 ∠-153.6° and 0.756 ∠-153.6°
Γ_L = 2.469 ∠160.7° and 0.405 ∠160.7°
Magnitude: The magnitude of the reflection coefficient (Γ) ranges from 0 to 1. A value of 0 indicates no reflection (perfect matching), while a value of 1 indicates total reflection (complete mismatch).
Phase: The phase of the reflection coefficient provides information about the phase shift between the incident and reflected waves.
C. Power Gain
Power gain is defined as the ratio of the output power to the input power and is typically expressed in decibels (dB).[2] Transducer power gain 〖(G〗_T) is a specific type of power gain that measures how effectively an amplifier transfers power from the source to the load and is given by:
G_T=G_S G_0 G_L (5)
Where,
■(G_S=(1-|Γ_S |^2)/|1-Γ_“in " Γ_S |^2 ,@G_0=|S_21 |^2;@G_L=(1-|Γ_L |^2)/|1-S_22 Γ_L |^2 ,)
C.1. Design for maximum gain (conjugate matching)
For any given transistor the G_0 is fixed, the total gain of the amplifier is determined by G_L and G_S of the mathing sections [2].
Assuming lossless metching sections,
G_Tmax= (1-|Γ_S |^2)/|1-Γ_“in " Γ_S |^2 |S_21 |^2 (1-|Γ_L |^2)/|1-S_22 Γ_L |^2 (6)
By replacing the values of S-parameters and the reflection coefficient from the equations to the gain equations 4, we are able to define the Transducer power gain:
G_Tmax = 12.5 dB