SLUA560D June 2011 – March 2022 UCC28950 , UCC28950-Q1 , UCC28951 , UCC28951-Q1

12 Voltage Loop and Slope Compensation

The UCC28950/1 VREF output (Pin 1) needs a high frequency bypass capacitor to filter out high frequency noise. This pin needs at least 1 µF of high frequency bypass capacitance (C_BP1). Please refer to figure 1 for proper placement.

Equation 96.

C_{B P 1} = 1 u F

The voltage amplifier reference voltage (Pin 2, EA +) can be set with a voltage divider (R_A, R_B), for this design example we are going to set the error amplifier reference voltage (V1) to 2.5 V. Select a standard resistor value for R_B and then calculate resistor value R_A.

UCC28950/1/1 reference voltage:

Equation 97.

V_{R E F} = 5 V

Set voltage amplifier reference voltage:

Equation 98.

V 1 = 2.5 V

Equation 99.

R_{B} = 2.37 k Ω

Equation 100.

R_{A} = \frac{R_{B} \times (V_{R E F} - V 1)}{V 1} = 2.37 k Ω

Voltage divider formed by resistor R_C and R_I are chosen to set the DC output voltage (V_OUT) at Pin 3 (EA-).

Select a standard resistor for R_C:

Equation 101.

R_{C} = 2.37 k Ω

Calculate R_I:

Equation 102.

R_{I} = \frac{R c \times (V_{O U T} - V 1)}{V 1} \approx 9 k Ω

Then choose a standard resistor for R_I:

Equation 103.

R_{I} = 9.09 k Ω

Compensating the feedback loop can be accomplished by properly selecting the feedback components (R_F, C_Z and C_P). These components are placed as close to pin 3 and 4 as possible of the UCC28950/1.

Calculate load impedance at 10% load (R_LOAD):

Equation 104.

R_{L O A D} = \frac{{V_{O U T}}^{2}}{P_{O U T} \times 0.1} = 2.4 Ω

Approximation of control to output transfer function (G_CO(f)) as a function of frequency:

Equation 105.

G_{C O (f)} \approx \frac{Δ V_{O U T}}{Δ V_{C}} = a 1 \times a 2 \times \frac{R_{L O A D}}{R_{S}} \times (\frac{1 + 2 π j \times f \times E S R_{C O U T} \times C_{O U T}}{1 + 2 π j \times f \times R_{L O A D} \times C_{O U T}}) \times \frac{1}{1 + \frac{S (f)}{2 π \times f_{P P}} + {(\frac{S (f)}{2 π \times f_{P P}})}^{2}}

Double pole frequency of G_CO(f):

Equation 106.

f_{P P} \approx \frac{f s}{4} = 50 k H z

Angular velocity:

Equation 107.

S (f) = 2 π \times j \times f

Compensate the voltage loop with type 2 feedback network. The following transfer function is the compensation gain as a function of frequency (G_C(f)). Please refer to Figure 2-1 for component placement.

Equation 108.

G_{C (f)} = \frac{Δ V_{C}}{Δ V_{O U T}} = \frac{2 π j \times f \times R_{F} \times C_{Z} + 1}{2 π j \times f \times (C_{Z} + C_{P}) R_{I} (\frac{2 π j \times f \times C_{Z} \times C_{P} \times R_{F}}{C_{Z} + C_{P}} + 1)}

Equation 109.

Calculate voltage loop feedback resistor (R_F) based on crossing the voltage (f_C) loop over at a 10^th of the double pole frequency (f_PP).

Equation 110.

f_{C} = \frac{f_{P P}}{10} = 5 k H z

Equation 111.

R_{F} = \frac{R_{I}}{G_{C O} (\frac{f_{P P}}{10})} \approx 27.9 k Ω

Select a standard resistor for R_F.

Equation 112.

R_{F} \approx 27.4 k Ω

Calculate the feedback capacitor (C_Z) to give added phase at crossover.

Equation 113.

C_{Z} = \frac{1}{2 \times π \times R_{F} \times \frac{f_{C}}{5}} \approx 5.8 n F

Equation 114.

C_{Z} = 5.6 n F

Select a standard capacitance value for the design.

Put a pole at two times f_C.

Equation 115.

C_{P} = \frac{1}{2 \times π \times R_{F} \times f_{C} \times 2} \approx 580 p F

Select a standard capacitance value for the design.

Equation 116.

C_{P} = 560 p F

Loop gain as a function of frequency (T_V(f)) in dB.

Equation 117.

T_{V} d B (f) = 20 \log ((G_{C} (f) \times G_{C O} (f)))

Plot theoretical loop gain and phase to graphically check for loop stability (Figure 11-1). The theoretical loop gain crossed over at roughly 3.7 kHz with a phase margin of greater than 90 degrees.

Note:

It is wise to check your loop stability of your final design with transient testing and/or a network analyzer and adjust the compensation (G_C(f)) feedback as necessary.

Figure 12-1 Loop Gain and Loop Phase

To limit over shoot during power up the UCC28950/1 has a soft-start function (SS, Pin 5) which in this application was set for a soft start time of 15 ms (t_SS).

Equation 118.

t_{s s} = 15 m s

Equation 119.

C_{s s} = \frac{t_{s s} \times 25 u A}{V 1 + 0.55} \approx 123 n F

Select a standard capacitor for the design.

Equation 120.

C_{s s} = 150 n F

The UCC28950/1 also provides slope compensation for peak current mode control (Pin 12). This can be set by setting R_SUM with the following equations. The following equations will calculate the required amount of slope compensation (V_SLOPE) that is needed for loop stability.

Note:

The change in magnetizing current on the primary ΔIL_MAG contributes to slope compensation.

Equation 121.

∆ I L_{M A G} = \frac{V_{I N} (1 - D_{T Y P})}{L_{M A G} \times f s} = 234 m A

To help improve noise immunity V_SLOPE is set to have a total slope that will equal 10% of the maximum current sense signal (0.2 V) over one inductor switching period.

Equation 122.

V_{S L O P E 1} = 0.2 V \times f s \times \frac{0.04 V}{u s}

Equation 123.

V_{S L O P E 2} = 0.2 V \times f s - \frac{(\frac{∆ I L_{O U T}}{a 1 \times 2} - ∆ I L_{M A G}) \times R_{S} (1 - D_{T Y P}) \times f_{S}}{a 2} = \frac{0.04 V}{u s}

If V_SLOPE2 < V_SLOPE1 set V_SLOPE = V_SLOPE1

If V_SLOPE2 ≥ V_SLOPE1 set V_SLOPE = V_SLOPE2

Equation 124.

R_{S U M} = \frac{2.5 V \times 1 0^{3} Ω}{V_{S L O P E} \times 0.5 u s} \approx 125.4 k Ω

Select a standard resistor for R_SUM.

Equation 125.

R_{S U M} = 127 k Ω