How to design active RF Mixer Design with BJT

In RF electronics, RF mixers play a crucial role in signal processing, particularly in communication systems. One such mixer design is the active mixer using a BC547 transistor , which combines two input signals (a message signal and a carrier signal) to produce new frequency components. This article dives deep into the functionality of this circuit, how it works, the calculation of component values, and the governing equations that explain the mixing process.

What is an Active Mixer?

An active mixer is a nonlinear circuit that combines two input signals to generate output signals at the sum and difference frequencies of the inputs. Unlike passive mixers as illustrated in diode modulator, active mixers use an amplifying device (such as a transistor) to boost the mixed signals, making them more suitable for low-power applications. Following is the circuit diagram of active mixer using BJT transistor.

The circuit described here uses a BC547 NPN transistor as the active element. It is designed to mix a message signal (e.g., 1 kHz) with a carrier signal (e.g., 100 kHz) to produce output signals at:

• Sum frequency : $f_c+f_m$
• Difference frequency : $f_c-f_m$

This type of mixer is commonly referred to as a single-balanced active mixer because the carrier and message signals are applied to the base of the transistor, while the output is taken from the collector through a transformer.

How Does the Circuit Work?

Circuit Overview

1. Message and Carrier Signals : Both signals are applied to the base of the BC547 transistor through coupling capacitors and series resistors.
2. Biasing Network : A voltage divider (R1 and R2) provides DC bias to the base, ensuring the transistor operates in its active region. See how to bias a Bipolar Junction Transistor using Voltage Divider Biasing Technique.
   
3. Emitter Resistor (R3) : Stabilizes the operating point and provides negative feedback.
4. Emitter Bypass Capacitor (C1) : Bypasses AC signals to ground, effectively grounding the emitter for AC signals.
5. Collector Transformer : A center-tapped transformer couples the mixed signals to the output while providing impedance matching.

Mixing Process

The key to mixing lies in the nonlinear behavior of the transistor. When both the message and carrier signals are applied to the base, the transistor's exponential relationship between base-emitter voltage ($V_{BE}$) and collector current ($I_C$) generates new frequency components. These include:

• The original frequencies ($f_c$ and $f_m$)
• Sum frequency ($f_c+f_m$)
• Difference frequency ($f_c-f_m$)

The transformer at the collector isolates these mixed signals and provides the desired output.

How Are Component Values Calculated?

1. Biasing Network (R1, R2, and R3)

• Goal : Set the quiescent collector current ($I_C$) to approximately $1\text{mA}$.
• Emitter Voltage ($V_E$) : Assume $V_E=1\text{V}$, so:$$R3=\frac{V_E}{I_E}=\frac{1\text{V}}{1\text{mA}}=1\text{k}\Omega$$
• Base Voltage ($V_B$) : $V_B=V_E+V_{BE}=1\text{V}+0.7\text{V}=1.7\text{V}$.
• Use the voltage divider rule to calculate $R1$ and $R2$:$$\frac{R2}{R1+R2}=\frac{V_B}{V_{CC}}$$Substituting $V_B=1.7\text{V}$ and $V_{CC}=5\text{V}$:$$R1=18\text{k}\Omega ,R2=10\text{k}\Omega$$

2. Emitter Bypass Capacitor (C1)

• Ensure low reactance at the lowest frequency of interest ($f_m=1\text{kHz}$):$$C1\ge \frac{1}{2\pi fR3}=\frac{1}{2\pi \cdot 1000\cdot 1000}\approx 1.59\mu \text{F}$$Choose:$$C1=2.2\mu \text{F}$$

3. Coupling Capacitors

• For the message signal ($f_m=1\text{kHz}$):$$C_{\text{coupling, message}}=2.2\mu \text{F}$$
• For the carrier signal ($f_c=100\text{kHz}$):$$C_{\text{coupling, carrier}}=2.2\text{nF}$$

4. Collector Transformer Capacitors (C2 and C3)

• Resonate with the transformer's primary inductance ($L_p=100\mu \text{H}$) at $f_c=100\text{kHz}$:$$C2=C3=\frac{1}{(2\pi f_c{)}^2{L}_p}\approx 253\text{pF}$$Choose:$$C2=C3=270\text{pF}$$

Governing Equation: The Mixing Process

The mixing process is governed by the nonlinear relationship between the base-emitter voltage ($V_{BE}$) and the collector current ($I_C$). The collector current can be approximated by:

Where:

• $I_S$ is the saturation current of the transistor.
• $V_T$ is the thermal voltage ($\approx 26\text{mV}$).
• $V_{BE}$ is the base-emitter voltage.

When two input signals are applied to the base:

Expanding $e^{V_{BE}/V_T}$ using a Taylor series introduces product terms that generate the sum ($f_c+f_m$) and difference ($f_c-f_m$) frequencies. Thus, the output contains:

Applications of the Active Mixer

This circuit is widely used in:

• Radio receivers : To down-convert RF signals to intermediate frequency (IF) signals.
• Frequency modulation (FM) : To generate modulated signals.
• Signal processing : To combine or separate signals at different frequencies.

Conclusion

The active mixer using a BC547 transistor is a versatile and efficient circuit for combining two signals into new frequency components. By carefully selecting component values—such as resistors, capacitors, and the transformer—you can ensure optimal performance for your specific application. Understanding the governing equation and the nonlinear behavior of the transistor is key to mastering the design and functionality of this circuit. 

Further reading

If you are interested in learning other methods of building RF mixers see the following guides.

• How to design Differential RF Mixer
• What are different ways to build RF mixer?
• How MC1496 Balanced Modulator Works?(DSB-SC AM)