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Reference compensation circuit in TL431
**Introduction**
The TL431 is a three-terminal, adjustable precision voltage reference integrated circuit developed by Texas Instruments. It is known for its excellent thermal stability and is widely used in various electronic applications as a voltage regulator. The output voltage of the TL431 can be set to a desired value, typically starting from 2.5V (Vref), using two external resistors. This makes it suitable for a wide range of voltages up to 36V. The internal bandgap reference ensures high accuracy and stability, which are crucial for the overall performance of the system. Therefore, a stable and accurate reference voltage plays a vital role in the functionality of the entire device.
**1. Temperature Compensated Reference Source**
A highly precise reference source is employed in this design, as shown in Figure 1. Compared to traditional reference circuits, this design incorporates nonlinear temperature compensation, including exponential curvature compensation and second-order compensation. These improvements help maintain a stable reference voltage across a wide temperature range.
Figure 1: TL431 Schematic
As illustrated in Figure 2, the circuit includes curvature compensation to enhance temperature stability. In this configuration, resistors R3 and R2 have equal voltage drops, with a resistance ratio of R3:R2 = 3:1. The current through these resistors, I3 and I2, follows a ratio of 1:3. The current through resistor R1 is the sum of I3 and I2, given by I1 = I3 + I2.
The reference voltage equation for the circuit is:
$$ V_{\text{ref}} = V_{\text{be1}} + V_{\text{be3}} + I_1 R_1 + I_2 R_2 \quad (1) $$
Using Kirchhoff's Voltage Law (KVL), the current through resistor R3 can be calculated. Since $ I_b = I_c / \beta $, where β is the transistor’s current gain, the expression for I3 becomes:
$$ I_3 = \frac{\beta V_T \ln M}{R_5 + (\beta + 1) R_4} \quad (2) $$
Here, M represents the area ratio of the emitter regions of Q3 and Q4. Once I3 is determined, I1 and I2 can be derived accordingly. Finally, the reference voltage expression is:
$$ V_{\text{ref}} = \left( \frac{3}{4} V_{\text{be}} + \frac{1}{4} V_g \right) + \frac{1}{4} \alpha T - \frac{1}{4} \gamma \ln T \quad (3) $$
In this formula, both $ V_{\text{be}} $ and β are temperature-dependent variables. Their expressions are:
$$ V_{\text{be}} = V_{g0} - \alpha T + \gamma \ln T \quad (4) $$
$$ \beta = \alpha' T + \gamma' \quad (5) $$
Where α, γ, α', and γ' are process-dependent but temperature-independent constants. Substituting equations (4) and (5) into equation (1) gives the final reference voltage as a function of temperature:
$$ V_{\text{ref}} = A + B T + K_1 T^2 + K_2 \ln T \quad (6) $$
This expression consists of three parts: a constant term, a linear term, and a nonlinear term. The linear and nonlinear terms are defined as:
$$ \text{Linear Term} = B T $$
$$ \text{Nonlinear Term} = K_1 T^2 + K_2 \ln T $$
By adjusting the resistor values, the coefficients K1 and K2 can be optimized to achieve a more stable and accurate reference voltage over a wide temperature range. This design ensures that the TL431 maintains high performance even under varying environmental conditions.