SLUAAL2 Application note

SLUAAL2 june 2023 UCC256402 , UCC256403 , UCC256404

1.11.2.3 Type 3 Compensator with Fast Lane

Figure 1-25 Type 3 Compensator with Fast Lane

Equation 47.

G_{c} (s) = |\frac{V_{f b} (s)}{V_{o} (s)}| = R_{f b} C T R (\frac{1}{(C_{v} + C_{f}) \cdot R_{u p}} \frac{1 + R_{v} C_{v} s}{(1 + \frac{s R_{v} C_{v} C_{f}}{C_{v} + C_{f}}) s} + 1) (\frac{1 + s C_{p} (R_{L E D} + R_{p})}{R_{L E D} (1 + R_{p} C_{p} s)})

Equation 48.

\begin{array}{l} Assuming C_{f} < < C_{v}, G_{c} (s) further simplifies to \\ G_{c} (s) = \frac{R_{f b} C T R}{R_{L E D}} (\frac{1}{C_{v} \cdot R_{u p}} \frac{1 + R_{v} C_{v} s}{(1 + s R_{v} C_{f}) s} + 1) (\frac{1 + s C_{p} (R_{L E D} + R_{p})}{1 + R_{p} C_{p} s}) \end{array}

Equation 49.

This can be written as G_{c} (s) = G_{o} (\frac{\frac{ω_{L}}{s} + 1}{1 + \frac{s}{ω_{p 1}}}) (\frac{1 + \frac{s}{ω_{z}}}{1 + \frac{s}{ω_{p 2}}})

Equation 50.

\begin{array}{l} where G_{o} = \frac{R_{f b} C T R}{R_{L E D}} (1 + \frac{R_{v}}{R_{u p}}) ω_{L} = \frac{1}{(R_{v} + R_{u p}) \cdot C_{v}} ω_{p 1} = \frac{1}{R_{v} \cdot C_{f}} \\ ω_{z} = \frac{1}{(R_{L E D} + R_{p}) \cdot C_{p}} ω_{p 2} = \frac{1}{R_{p} \cdot C_{p}} \end{array}

Here assuming $ω_{L} ≪ ω_{z} ≪ ω_{c} ≪ ω_{p 2} ≪ ω_{p 1}$ , $ω_{z}$ and $ω_{p 2}$ creates the phase lead whereas $ω_{L}$ implements the integrator to reduce the steady state error, and $ω_{p1}$ eliminates the effect of high frequency noise on the control loop. Here $ω_{c}$ is cross over frequency.