Feedback topologies and architecture explained

Feedback refers to a core concept in circuit design and control theory, used to stabilize amplifiers and control system behavior. This article outlines the fundamental architecture of feedback, classifies standard topologies, and examines a practical hardware implementation as a case study.

What is the fundamental architecture of a feedback system?

A feedback system consists of a feedforward amplifier with an open-loop gain (A_v) and a feedback network with a factor (B). The system subtracts a portion of the output signal from the input signal to generate an error signal, which is subsequently amplified.

As shown in Figure 1, the architecture illustrates the signal flow. The signal flows from the input (V_in) through the adder to the amplifier (A_v) to generate the output (V_out). The feedback block (B) samples the output and returns it to the adder. The diagram indicates that the feedback signal is subtracted from the input, constituting the negative polarity required for stability. This structure forces the output to track the input according to the feedback factor B.

For a negative feedback system, the closed-loop gain A_CL is defined as:

A_CL = A_v/(1+A_vB)

The open-loop gain A_v in operational amplifiers is normally high but subject to variation due to temperature fluctuations and manufacturing processes. However, in a closed-loop configuration, if the loop gain (A_vB) is sufficiently large, the transfer function approximates 1/B.

This effect, known as gain desensitization, makes the system’s performance dependent on the passive components of the feedback network rather than the parameters of the active device. In other words, precision is achieved through the feedback network.

How are feedback topologies classified?

Feedback topologies are classified based on the Sense mechanism (how the output is sampled) and the Return mechanism (how the signal is combined at the input). One of the key aspects deals with impedance transformation.

Figure 2 displays the four primary configurations:

1. Voltage-Voltage feedback: The feedback network samples voltage in parallel at the output and mixes it in series at the input. The series mixing increases input impedance, which means it is appropriate for voltage sensing.
2. Voltage-Current feedback: Known as the Transimpedance topology, this configuration uses a parallel connection at the input (I_in node). This results in reduced input impedance, facilitating current sensing from sources such as photodiodes.
3. Current-Voltage feedback: This topology samples output current in series. The loop passes through the load, increasing output impedance and stabilizing the current drive.
4. Current-Current feedback: This configuration samples output current and returns input current, functioning as a current amplifier.

Case study

Precision instrumentation, such as optical receivers, often must manage wide dc dynamic ranges. When it comes to sensor interfaces, stability cannot be compromised.

In a standard Capacitive Feedback Transimpedance Amplifier (CF-TIA), a resistor in the dc feedback loop drains background dc currents. To handle high maximum dc inputs without saturation, this resistor must have a low value. However, low-value resistors generate higher thermal noise, which impacts the Signal-to-Noise Ratio at low dc input levels.

To address this, designs may replace the static resistor with a transistor (BJT or FET) in the feedback loop. The transistor functions as a variable current sink. The thermal noise of the resistor is replaced by the shot noise of the transistor. Since shot noise scales with current, the noise floor remains lower during normal operation (low dc input) compared to the constant noise of a static low-value resistor. For example, replacing a resistor with a BJT allows for a wider dynamic range.

Figure 3 demonstrates the physical layout of a CF-TIA. The red box on the right indicates the dc feedback loop containing the transistor and compensation components. Placing these components in proximity to the integrator stage (left red box) minimizes parasitic capacitance. With this compensation, the CF-TIA maintains stability across a dynamic range of dc input currents, from picoamps to microamps.

Summary

Feedback allows for the control of active device characteristics. By selecting appropriate topologies and understanding the trade-offs between active and passive feedback networks, engineers can design systems optimized for noise performance, linearity, and stability.

References

A Capacitive Feedback Transimpedance Amplifier with a DC Feedback Loop Using a Transistor for High DC Dynamic Range, MDPI
Feedback | ECEN326: Electronic Circuits Spring 2022, Texas A&M University
2-2. Feedback (positive and negative feedback), Toshiba

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