SNVSAI4B November   2017  – November 2020 LM5145

PRODUCTION DATA  

  1. Features
  2. Applications
  3. Description
  4. Revision History
  5. Description (continued)
  6. Pin Configuration and Functions
    1. 6.1 Wettable Flanks
  7. Specifications
    1. 7.1 Absolute Maximum Ratings
    2. 7.2 ESD Ratings
    3. 7.3 Recommended Operating Conditions
    4. 7.4 Thermal Information
    5. 7.5 Electrical Characteristics
    6. 7.6 Switching Characteristics
    7. 7.7 Typical Characteristics
  8. Detailed Description
    1. 8.1 Overview
    2. 8.2 Functional Block Diagram
    3. 8.3 Feature Description
      1. 8.3.1  Input Range (VIN)
      2. 8.3.2  Output Voltage Setpoint and Accuracy (FB)
      3. 8.3.3  High-Voltage Bias Supply Regulator (VCC)
      4. 8.3.4  Precision Enable (EN/UVLO)
      5. 8.3.5  Power Good Monitor (PGOOD)
      6. 8.3.6  Switching Frequency (RT, SYNCIN)
        1. 8.3.6.1 Frequency Adjust
        2. 8.3.6.2 Clock Synchronization
      7. 8.3.7  Configurable Soft Start (SS/TRK)
        1. 8.3.7.1 Tracking
      8. 8.3.8  Voltage-Mode Control (COMP)
      9. 8.3.9  Gate Drivers (LO, HO)
      10. 8.3.10 Current Sensing and Overcurrent Protection (ILIM)
      11. 8.3.11 OCP Duty Cycle Limiter
    4. 8.4 Device Functional Modes
      1. 8.4.1 Shutdown Mode
      2. 8.4.2 Standby Mode
      3. 8.4.3 Active Mode
      4. 8.4.4 Diode Emulation Mode
      5. 8.4.5 Thermal Shutdown
  9. Application and Implementation
    1. 9.1 Application Information
      1. 9.1.1 Design and Implementation
      2. 9.1.2 Power Train Components
        1. 9.1.2.1 Inductor
        2. 9.1.2.2 Output Capacitors
        3. 9.1.2.3 Input Capacitors
        4. 9.1.2.4 Power MOSFETs
      3. 9.1.3 Control Loop Compensation
      4. 9.1.4 EMI Filter Design
    2. 9.2 Typical Applications
      1. 9.2.1 Design 1 – 20-A High-Efficiency Synchronous Buck Regulator for Telecom Power Applications
        1. 9.2.1.1 Design Requirements
        2. 9.2.1.2 Detailed Design Procedure
        3. 9.2.1.3 Custom Design With WEBENCH® Tools
        4. 9.2.1.4 Application Curves
      2. 9.2.2 Design 2 – High Density, 12-V, 10-A Rail With LDO Low-Noise Auxiliary Output for RF Power Applications
        1. 9.2.2.1 Design Requirements
        2. 9.2.2.2 Detailed Design Procedure
        3. 9.2.2.3 Application Curves
      3. 9.2.3 Design 3 – 150-W, Regulated 24-V Rail for Commercial Drone Applications With Output Voltage Tracking Feature
        1. 9.2.3.1 Design Requirements
        2. 9.2.3.2 Detailed Design Procedure
        3. 9.2.3.3 Application Curves
      4. 9.2.4 Design 4 – Powering a Multicore DSP From a 24-V or 48-V Rail
        1. 9.2.4.1 Design Requirements
        2. 9.2.4.2 Detailed Design Procedure
        3. 9.2.4.3 Application Curves
  10. 10Power Supply Recommendations
  11. 11Layout
    1. 11.1 Layout Guidelines
      1. 11.1.1 Power Stage Layout
      2. 11.1.2 Gate Drive Layout
      3. 11.1.3 PWM Controller Layout
      4. 11.1.4 Thermal Design and Layout
      5. 11.1.5 Ground Plane Design
    2. 11.2 Layout Example
  12. 12Device and Documentation Support
    1. 12.1 Device Support
      1. 12.1.1 Third-Party Products Disclaimer
      2. 12.1.2 Development Support
      3. 12.1.3 Custom Design With WEBENCH® Tools
    2. 12.2 Documentation Support
      1. 12.2.1 Related Documentation
        1. 12.2.1.1 PCB Layout Resources
        2. 12.2.1.2 Thermal Design Resources
    3. 12.3 Receiving Notification of Documentation Updates
    4. 12.4 Support Resources
    5. 12.5 Trademarks
    6. 12.6 Electrostatic Discharge Caution
    7. 12.7 Glossary
  13. 13Mechanical, Packaging, and Orderable Information

Control Loop Compensation

The poles and zeros inherent to the power stage and compensator are respectively illustrated by red and blue dashed rings in the schematic embedded in Table 9-2.

Table 9-2 Buck Regulator Poles and Zeros
GUID-37F89074-CF33-447B-8D5F-47E757DF7B25-low.gif
POWER STAGE POLES POWER STAGE ZEROS COMPENSATOR POLES COMPENSATOR ZEROS
GUID-9F627E66-4834-4C4A-AE40-F4461F9495DF-low.gif GUID-816CC8AC-C600-4BED-9D65-70A42DFB2B50-low.gif GUID-ED91DE32-D435-416A-A86D-814938CD4060-low.gif GUID-2A66132C-59A4-4B5E-80A3-5AC5496A4D7D-low.gif
GUID-DA66B55A-A6E1-4852-B1F3-683CB308D2D1-low.gif GUID-F1CD1D41-D2B2-4BCC-97A7-44E9D8FB5AB1-low.gif GUID-C39ED1A2-E45A-4679-B931-DBD12CEBD716-low.gif

The compensation network typically employed with voltage-mode control is a Type-III circuit with three poles and two zeros. One compensator pole is located at the origin to realize high DC gain. The normal compensation strategy uses two compensator zeros to counteract the LC double pole, one compensator pole located to nullify the output capacitor ESR zero, with the remaining compensator pole located at one-half switching frequency to attenuate high frequency noise. The resistor divider network to FB determines the desired output voltage. Note that the lower feedback resistor, RFB2, has no impact on the control loop from an AC standpoint because the FB node is the input to an error amplifier and is effectively at AC ground. Hence, the control loop is designed irrespective of output voltage level. The proviso here is the necessary output capacitance derating with bias voltage and temperature.

The small-signal open-loop response of a buck regulator is the product of modulator, power train and compensator transfer functions. The power stage transfer function can be represented as a complex pole pair associated with the output LC filter and a zero related to the ESR of the output capacitor. The DC (and low frequency) gain of the modulator and power stage is VIN/VRAMP. The gain from COMP to the average voltage at the input of the LC filter is held essentially constant by the PWM line feedforward feature of the LM5145 (15 V/V or 23.5 dB).

Complete expressions for small-signal frequency analysis are presented in Table 9-3. The transfer functions are denoted in normalized form. While the loop gain is of primary importance, a regulator is not specified directly by its loop gain but by its performance related characteristics, namely closed-loop output impedance and audio susceptibility.

Table 9-3 Buck Regulator Small-Signal Analysis
TRANSFER FUNCTION EXPRESSION
Open-loop transfer function GUID-5821C011-FE46-4D12-8FFB-89252515AF0C-low.gif
Duty-cycle-to-output transfer function GUID-99B231EB-F6AB-4F6F-BF45-9F3EE4B334BB-low.gif
Compensator transfer function(1) GUID-39D9E1CF-B647-4C32-91B9-F5318803ECBB-low.gif
Modulator transfer function GUID-2F1530B8-4ABD-410A-A3E1-A26E0D6E3EF6-low.gif
Kmid = RC1/RFB1 is the mid-band gain of the compensator. By expressing one of the compensator zeros in inverted zero format, the mid-band gain is denoted explicitly.

Figure 9-2 shows the open-loop response gain and phase. The poles and zeros of the system are marked with x and o symbols, respectively, and a + symbol indicates the crossover frequency. When plotted on a log (dB) scale, the open-loop gain is effectively the sum of the individual gain components from the modulator, power stage, and compensator (see Figure 9-3). The open-loop response of the system is measured experimentally by breaking the loop, injecting a variable-frequency oscillator signal, and recording the ensuing frequency response using a network analyzer setup.

GUID-773AEF14-DC45-4190-8906-0B0CF6A598AE-low.gifFigure 9-2 Typical Buck Regulator Loop Gain and Phase With Voltage-Mode Control

If the pole located at ωp1 cancels the zero located at ωESR and the pole at ωp2 is located well above crossover, the expression for the loop gain, Tv(s) in Table 9-3, can be manipulated to yield the simplified expression given in Equation 14.

Equation 14. GUID-DDC6CD96-AC4A-4D83-929D-8CD667C73FF2-low.gif

Essentially, a multi-order system is reduced to a single-order approximation by judicious choice of compensator components. A simple solution for the crossover frequency (denoted as fc in Figure 9-2) with Type-III voltage-mode compensation is derived as shown in Equation 15 and Equation 16.

Equation 15. GUID-03223E9E-4C1D-47E9-A13F-9A116AFDB97F-low.gif
Equation 16. GUID-9CEB0374-D0F8-4C76-92FB-DC7B73680F34-low.gif
GUID-DB60CCEE-16B0-4096-8080-3C24EADB0654-low.gifFigure 9-3 Buck Regulator Constituent Gain Components

The loop crossover frequency is usually selected between one-tenth to one-fifth of switching frequency. Inserting an appropriate crossover frequency into Equation 16 gives a target for the mid-band gain of the compensator, Kmid. Given an initial value for RFB1, RFB2 is then selected based on the desired output voltage. Values for RC1, RC2, CC1, CC2, and CC3 are calculated from the design expressions listed in Table 9-4, with the premise that the compensator poles and zeros are set as follows: ωz1 = 0.5·ωo, ωz2 = ωo, ωp1 = ωSW/2, and ωp2 = ωESR.

Table 9-4 Compensation Component Selection
RESISTORS CAPACITORS
GUID-1937625C-5B07-4CA2-A94E-2700DF008847-low.gif GUID-BCDD8F71-4C1B-443E-A58D-7EA202F2F1B1-low.gif
GUID-4B2F3BC5-63AB-46BE-AC3D-B0643A3CE9C1-low.gif GUID-40F4AC79-1C4D-48F1-A2CF-5A076FCBA973-low.gif
GUID-BA506F6D-D434-4A62-82D2-4975365FA37F-low.gif GUID-1D721947-4B4C-4FCE-A7B1-BB868AE3A6F0-low.gif

Referring to the bode plot in Figure 9-2, the phase margin, indicated as φM, is the difference between the loop phase and –180° at crossover. A target of 50° to 70° for this parameter is considered ideal. Additional phase boost is dialed in by locating the compensator zeros at a frequency lower than the LC double pole (hence why CC1 is scaled by a factor of 2 above). This helps mitigate the phase dip associated with the LC filter, particularly at light loads when the Q-factor is higher and the phase dip becomes especially prominent. The ramification of low phase in the frequency domain is an under-damped transient response in the time domain.

The power supply designer now has all the necessary expressions to optimally position the loop crossover frequency while maintaining adequate phase margin over the required line, load and temperature operating ranges. The LM5145 Quickstart Calculator is available to expedite these calculations and to adjust the bode plot as needed.