How to design Small Signal RF Amplifier?

A small-signal RF amplifier is a type of electronic amplifier designed to boost low-power radio frequency (RF) signals without significantly distorting them. It is called "small-signal" because it operates with input signals that are small enough to keep the amplifier in its linear region, meaning the output signal is a scaled-up version of the input signal without clipping or distortion.

What is a Small-Signal RF Amplifier?

• Purpose: It amplifies weak RF signals (e.g., from an antenna, sensor, or another RF source) to a higher power level while maintaining signal integrity.

• Applications: Used in communication systems (e.g., radios, TVs, cell phones), radar systems, wireless devices, and test equipment.

• Key Characteristics:

  • Operates in the linear region of the transistor or active device.

  • Designed for low noise and high gain.

  • Typically handles low-power signals (milliwatts or less).

Typical Amplitude and Frequency of Input and Output Signals

Input Signal

• Amplitude: The input signal is typically very small, often in the range of microvolts (µV) to millivolts (mV). For example:

  • In a radio receiver, the signal from the antenna might be as small as 1 µV to 1 mV.

• Frequency: The frequency range depends on the application, but small-signal RF amplifiers are commonly used in the RF and microwave range:

  • RF Range: 3 kHz to 300 MHz (e.g., AM/FM radio, TV broadcast).

  • Microwave Range: 300 MHz to 300 GHz (e.g., Wi-Fi, satellite communication, radar).

Output Signal

• Amplitude: The output signal is amplified but still relatively low-power, typically in the range of milliwatts (mW). For example:

  • A small-signal RF amplifier might boost a 1 mV input signal to 100 mV (or more), depending on the gain.

• Frequency: The output signal has the same frequency as the input signal but at a higher amplitude. The amplifier does not change the frequency of the signal.

Key Parameters of a Small-Signal RF Amplifier

Example Scenario

Imagine you’re designing a small-signal RF amplifier for a 250 MHz radio receiver:

• Input Signal: A weak signal from the antenna, say 10 µV at 250 MHz.

• Output Signal: After amplification, the signal might be 1 mV at 250 MHz (a gain of 40 dB).

• Amplifier Role: The amplifier boosts the signal to a level where it can be processed by the next stage (e.g., an RF mixer or RF demodulator) without adding significant noise or distortion.

Small Signal RF Amplifier Circuit Design Example

By following these steps, you can design a small-signal RF amplifier that provides 9 dB gain at 250 MHz. The key steps are:

1. Checking stability and calculating key parameters.
2. Drawing the gain circle to find the right load impedance.
3. Designing the output matching network to move the load impedance onto the gain circle.
4. Designing the input matching network to ensure the source is properly matched.
5. Building the final circuit with the calculated components.

Step 1: Check Stability and Calculate Key Parameters

First, we need to make sure the transistor we’re using is stable. Stability is important because an unstable transistor can cause oscillations, which we don’t want in an amplifier. 

In this case, the transistor is unconditionally stable (a stability factor $K=1.033$ confirms this) which will be determined below.

Step 2: Draw the Gain Circle

We want a 9 dB gain, so we need to find the set of load impedances that will give us this gain. To do this, we draw a gain circle on the Smith Chart:

• Center of the circle:

  $$r_o=\frac{G\cdot C_2}{1+D^2\cdot G}=0.712\mathrm{\angle }33.9^{\circ }$$

• Radius of the circle:

  The radius \( \rho_0 \) is defined as:
  \[
  \rho_0 = \frac{1 - 2K G \left| S_{12} S_{21} \right| + 1 + D^2 G \left| D S \right|^2 G^2}{0.285}
  \]
  
  Any load impedance located on this circle will result in a gain of 9 dB, provided that the input is properly matched.

Step 3: Design the Output Matching Network

The load impedance we’re working with is $Z_L=50-j50\mathrm{\Omega }$. On the Smith Chart, this is represented as Point A (normalized to $1-j1$). To move this impedance onto the gain circle, we need to add some components:

1. Series capacitor $C_1$:$$C_1=\frac{1}{2\pi (250\text{MHz})\cdot 2\cdot 50}=6.4\text{pF}$$
2. Shunt inductor $L_1$: $$L_1=\frac{50}{2\pi (250\text{MHz})\cdot 0.425}=75\text{nH}$$

After adding these components, the load impedance moves to Point C on the gain circle ($0.82\mathrm{\angle }14.2^{\circ }$).

Step 4: Design the Input Matching Network

Now, we need to match the input of the transistor to the source impedance. The required source reflection coefficient is:

The actual source impedance is $Z_S=35-j60\mathrm{\Omega }$ (normalized to $0.7-j1.2$). To match this to the required ${\mathrm{\Gamma }}_S$, we add:

• Shunt capacitor $C_2=7.9\text{pF}$.
• Series inductor $L_2=34.7\text{nH}$.
• Shunt capacitor $C_3=27\text{pF}$.

Step 5: Final Circuit

The final amplifier circuit consists of:

• Output matching network: A series capacitor ($C_1=6.4\text{pF}$) and a shunt inductor ($L_1=75\text{nH}$).

• Input matching network: A shunt capacitor ($C_2=7.9\text{pF}$), a series inductor ($L_2=34.7\text{nH}$), and another shunt capacitor ($C_3=27\text{pF}$).

 The final circuit of the small signal RF amplifier is shown below.

This RF amplifier will now work efficiently at 250 MHz, giving us the desired gain while ensuring stability and proper impedance matching. Let me know if you have any questions!