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2 What impacts the LDO rise time?

Linear regulator references can use either a precision voltage source (Figure 2-1) or a precision current source (Figure 2-2). The linear regulator turn-on time is affected by either the reference turning on or the RC time constant formed by the R_TOP and C_FF in the feedback loop. Typically, the reference voltage turns on very quickly, however in modern LDO regulators the reference voltage may also be filtered through a low pass noise reduction (NR) resistor and capacitor.

TPS7A20, TPS7A21, TPS7A13, TPS7A14, TPS7A49, TPS7A91, TPS7A92, TLV702, TLV703, TLV755P, TPS7A52, TPS7A53, TPS7A53B, TPS7A54, TPS7A83A, TPS7A84A, TPS7A85A, TPS7A57, TPS7A94, TPS7A96, TPS7H1111-SP, TPS74401, TPS7A74, TPS74701, TPS74801, TPS74901 Precision voltage
reference

Figure 2-1 Precision voltage reference

Figure 2-2 Precision current reference

Voltage across the R_TOP resistor ramps in accordance with both the RC time constants on V_REF and R_TOP. Equation 2 represents the NR/SS time constant and Equation 3 represents the FF time constant.

Equation 2.

τ_{N R / S S} = R_{N R / S S} \times C_{N R / S S}

Equation 3.

τ_{F F} = R_{T O P} \times C_{F F}

During the turn-on period, the voltage on the VOUT pin is the summation of the voltage across the R_BOTTOM resistor (or V_FB) and the voltage across the R_TOP resistor (or V_TOP) as shown in Equation 4 :

Equation 4.

V_{O U T} (t) = V_{T O P} (t) + V_{F B} (t)

During the turn-on period, the reference voltage ramps fast enough for it to approximate an ideal step function relative to the much longer $τ$ _NR/SS time constant. Equation 5 describes V_FB(t) when the LDO regulator reference is a precision voltage source, but when it is a precision current source, use Equation 6 instead.

Equation 5.

V_{F B} (t) = V_{R E F} \times (1 - e^{- \frac{t}{τ_{N R / S S}}})

Equation 6.

V_{F B} (t) = I_{N R / S S} \times R_{N R / S S} \times (1 - e^{- \frac{t}{τ_{N R / S S}}})

The voltage across the top set point resistor is more complex to calculate as V_FB(t) is not always a step function. When $τ$ _NR/SS and $τ$ _FF are comparable values, neither time constant dominates the turn-on calculation. Use Laplace transforms and partial fraction expansions [1]-[2] to derive V_TOP(t), shown in Equation 7.

Equation 7.

V_{T O P} (t) = V_{R E F} \times \frac{R_{T O P}}{R_{B O T T O M}} \times (1 - \frac{τ_{N R / S S}}{τ_{N R / S S} - τ_{F F}} \times e^{\frac{- t}{τ_{N R / S S}}} - \frac{τ_{F F}}{τ_{F F} - τ_{N R / S S}} {\times e}^{\frac{- t}{τ_{F F}}})