SNVS276I April   2004  – February 2019 LM2743

PRODUCTION DATA.  

  1. 1 Features
  2. 2 Applications
  3. 3 Description
    1.     Device Images
      1.      Typical Application Diagram
  4. 4 Revision History
  5. 5 Pin Configuration and Functions
    1.     Pin Functions
  6. 6 Specifications
    1. 6.1 Absolute Maximum Ratings
    2. 6.2 ESD Ratings
    3. 6.3 Recommended Operating Conditions
    4. 6.4 Thermal Information
    5. 6.5 Electrical Characteristics
    6. 6.6 Typical Characteristics
  7. 7 Detailed Description
    1. 7.1 Overview
    2. 7.2 Functional Block Diagram
    3. 7.3 Feature Description
      1. 7.3.1  Start Up and Soft-Start
      2. 7.3.2  Normal Operation
      3. 7.3.3  Tracking a Voltage Level
      4. 7.3.4  Tracking Voltage Slew Rate
      5. 7.3.5  Sequencing
      6. 7.3.6  SD Pin Impedance
      7. 7.3.7  MOSFET Gate Drivers
      8. 7.3.8  Power Good Signal
      9. 7.3.9  UVLO
      10. 7.3.10 Current Limit
      11. 7.3.11 Foldback Current Limit
    4. 7.4 Device Functional Modes
      1. 7.4.1 Shutdown
  8. 8 Application and Implementation
    1. 8.1 Application Information
    2. 8.2 Typical Applications
      1. 8.2.1 Synchronous Buck Converter Typical Application using LM2743
        1. 8.2.1.1 Design Requirements
        2. 8.2.1.2 Detailed Design Procedure
          1. 8.2.1.2.1 Custom Design With WEBENCH® Tools
          2. 8.2.1.2.2 Duty Cycle Calculation
          3. 8.2.1.2.3 Input Capacitor
          4. 8.2.1.2.4 Output Inductor
          5. 8.2.1.2.5 Output Capacitor
          6. 8.2.1.2.6 MOSFETs
          7. 8.2.1.2.7 Support Components
          8. 8.2.1.2.8 Control Loop Compensation
          9. 8.2.1.2.9 Efficiency Calculations
        3. 8.2.1.3 Application Curves
      2. 8.2.2 Example Circuit 1
        1. 8.2.2.1 Design Requirements
        2. 8.2.2.2 Detailed Design Procedure
        3. 8.2.2.3 Bill of Materials
      3. 8.2.3 Example Circuit 2
        1. 8.2.3.1 Design Requirements
        2. 8.2.3.2 Detailed Design Procedure
        3. 8.2.3.3 Bill of Materials
      4. 8.2.4 Example Circuit 3
        1. 8.2.4.1 Design Requirements
        2. 8.2.4.2 Detailed Design Procedure
        3. 8.2.4.3 Bill of Materials
  9. 9 Power Supply Recommendations
  10. 10Layout
    1. 10.1 Layout Guidelines
    2. 10.2 Layout Example
  11. 11Device and Documentation Support
    1. 11.1 Device Support
      1. 11.1.1 Development Support
        1. 11.1.1.1 Custom Design With WEBENCH® Tools
    2. 11.2 Receiving Notification of Documentation Updates
    3. 11.3 Community Resources
    4. 11.4 Trademarks
    5. 11.5 Electrostatic Discharge Caution
    6. 11.6 Glossary
  12. 12Mechanical, Packaging, and Orderable Information

Package Options

Mechanical Data (Package|Pins)
Thermal pad, mechanical data (Package|Pins)
Orderable Information

8.2.1.2.8 Control Loop Compensation

The LM2743 uses voltage-mode (‘VM’) PWM control to correct changes in output voltage due to line and load transients. One of the attractive advantages of voltage mode control is its relative immunity to noise and layout. However VM requires careful small signal compensation of the control loop for achieving high bandwidth and good phase margin.

The control loop is comprised of two parts. The first is the power stage, which consists of the duty cycle modulator, output inductor, output capacitor, and load. The second part is the error amplifier, which for the LM2743 is a 9-MHz op-amp used in the classic inverting configuration. Figure 32 shows the regulator and control loop components.

LM2743 20095264.gifFigure 32. Power Stage and Error Amplifier

One popular method for selecting the compensation components is to create Bode plots of gain and phase for the power stage and error amplifier. Combined, they make the overall bandwidth and phase margin of the regulator easy to see. Software tools such as Excel, MathCAD, and Matlab are useful for showing how changes in compensation or the power stage affect system gain and phase.

The power stage modulator provides a DC gain ADC that is equal to the input voltage divided by the peak-to-peak value of the PWM ramp. This ramp is 1.0VP-P for the LM2743. The inductor and output capacitor create a double pole at frequency fDP, and the capacitor ESR and capacitance create a single zero at frequency fESR. For this example, with VIN = 3.3 V, these quantities are:

Equation 30. LM2743 20095265.gif
Equation 31. LM2743 20095266.gif
Equation 32. LM2743 20095267.gif

In the equation for fDP, the variable RL is the power stage resistance, and represents the inductor DCR plus the on resistance of the top power MOSFET. RO is the output voltage divided by output current. The power stage transfer function GPS is given by the following equation, and Figure 34 shows Bode plots of the phase and gain in this example.

Equation 33. LM2743 20095268.gif

where

  • a = LCO(RO + RC)
  • b = L + CO(RORL + RORC + RCRL)
  • c = RO + RL
LM2743 20095269.gifFigure 33. Gain vs Frequency
LM2743 20095270.gifFigure 34. Power Stage Gain and Phase

The double pole at 4.5 kHz causes the phase to drop to approximately -130° at around 10 kHz. The ESR zero, at 20.3 kHz, provides a +90° boost that prevents the phase from dropping to -180º. If this loop were left uncompensated, the bandwidth would be approximately 10 kHz and the phase margin 53°. In theory, the loop would be stable, but would suffer from poor DC regulation (due to the low DC gain) and would be slow to respond to load transients (due to the low bandwidth.) In practice, the loop could easily become unstable due to tolerances in the output inductor, capacitor, or changes in output current, or input voltage. Therefore, the loop is compensated using the error amplifier and a few passive components.

For this example, a Type III, or three-pole-two-zero approach gives optimal bandwidth and phase.

In most voltage mode compensation schemes, including Type III, a single pole is placed at the origin to boost DC gain as high as possible. Two zeroes fZ1 and fZ2 are placed at the double pole frequency to cancel the double pole phase lag. Then, a pole, fP1 is placed at the frequency of the ESR zero. A final pole fP2 is placed at one-half of the switching frequency. The gain of the error amplifier transfer function is selected to give the best bandwidth possible without violating the Nyquist stability criteria. In practice, a good crossover point is one-fifth of the switching frequency, or 60 kHz for this example. The generic equation for the error amplifier transfer function is:

Equation 34. LM2743 20095271.gif

In this equation, the variable AEA is a ratio of the values of the capacitance and resistance of the compensation components, arranged as shown in Figure 32. AEA is selected to provide the desired bandwidth. A starting value of 80,000 for AEA should give a conservative bandwidth. Increasing the value will increase the bandwidth, but will also decrease phase margin. Designs with 45° to 60° are usually best because they represent a good trade-off between bandwidth and phase margin. In general, phase margin is lowest and gain highest (worst-case) for maximum input voltage and minimum output current. One method to select AEA is to use an iterative process beginning with these worst-case conditions.

  1. Increase AEA
  2. Check overall bandwidth and phase margin
  3. Change VIN to minimum and recheck overall bandwidth and phase margin
  4. Change IO to maximum and recheck overall bandwidth and phase margin

The process ends when the both bandwidth and the phase margin are sufficiently high. For this example input voltage can vary from 3.0 to 3.6 V and output current can vary from 0 to 4 A, and after a few iterations a moderate gain factor of 101 dB is used.

The error amplifier of the LM2743 has a unity-gain bandwidth of 9 MHz. In order to model the effect of this limitation, the open-loop gain can be calculated as:

Equation 35. LM2743 20095272.gif

The new error amplifier transfer function that takes into account unity-gain bandwidth is:

Equation 36. LM2743 20095273.gif

The gain and phase of the error amplifier are shown in Figure 36.

LM2743 20095274.gifFigure 35. Gain vs Frequency
LM2743 20095275.gifFigure 36. Error Amplifier Gain and Phase

In VM regulators, the top feedback resistor RFB2 forms a part of the compensation. Setting RFB2 to 10 kΩ, ±1% usually gives values for the other compensation resistors and capacitors that fall within a reasonable range. (Capacitances > 1 pF, resistances < 1 MΩ) CC1, CC2, CC3, RC1, and RC2 are selected to provide the poles and zeroes at the desired frequencies, using the following equations:

Equation 37. LM2743 20095276.gif
Equation 38. LM2743 20095277.gif
Equation 39. LM2743 20095278.gif
Equation 40. LM2743 20095279.gif
Equation 41. LM2743 20095280.gif

In practice, a good trade off between phase margin and bandwidth can be obtained by selecting the closest ±10% capacitor values above what are suggested for CC1 and CC2, the closest ±10% capacitor value below the suggestion for CC3, and the closest ±1% resistor values below the suggestions for RC1, RC2. Note that if the suggested value for RC2 is less than 100Ω, it should be replaced by a short circuit. Following this guideline, the compensation components will be:

 CC1 = 27 pF ±10%

 CC2 = 820 pF ±10%

 CC3 = 2.7 nF ±10%

 RC1 = 39.2 kΩ ±1%

 RC2 = 2.55 kΩ ±1%

 

The transfer function of the compensation block can be derived by considering the compensation components as impedance blocks ZF and ZI around an inverting op-amp:

Equation 42. LM2743 20095281.gif
Equation 43. LM2743 20095282.gif
Equation 44. LM2743 20095283.gif

As with the generic equation, GEA-ACTUAL must be modified to take into account the limited bandwidth of the error amplifier. The result is:

Equation 45. LM2743 20095284.gif

The total control loop transfer function H is equal to the power stage transfer function multiplied by the error amplifier transfer function.

Equation 46. H = GPS x HEA

 

The bandwidth and phase margin can be read graphically from Bode plots of HEA are shown in Figure 38.

LM2743 20095285.gifFigure 37. Gain vs Frequency
LM2743 20095286.gifFigure 38. Overall Loop Gain and Phase

The bandwidth of this example circuit is 59 kHz, with a phase margin of 60°.