Case Study: NJM2309 Application Circuit Design (PWM Step-down Converter) All Rights Reserved Copyright (C) Bee Technologies Corporation 20111

Contents Design Specification NJM2309 Typical Application Circuit Averaged Buck Switch Model Buck Regulator Design Workflow 1.Setting PWM Controller’s Parameters. 2.Programming Output Voltage: Rupper, Rlower 3.Inductor Selection: L 4.Capacitor Selection: C, ESR 5.Stabilizing the Converter Load Transient Response Simulation  Reference: Load Transient Response Simulation with PWM IC Transient Model Appendix A.Type 2 Compensation Calculation using Excel B.Feedback Loop Compensators C.Simulation Index All Rights Reserved Copyright (C) Bee Technologies Corporation 20112

Design Specification Step-Down (Buck) Converter : V IN, MAX = 32 (V) V IN, MIN = 6 (V) V OUT = 3.3 (V) V OUT, Ripple = 1% ( 33mV P-P ) I OUT, MAX = 1.0 (A) I OUT, MIN = 0.2 (A) Control IC : NJM2309 (Switching Regulator Control IC for Step-Down) Switching Frequency – fosc = 105 (kHz) All Rights Reserved Copyright (C) Bee Technologies Corporation NJM2309 Datasheet

NJM2309 Typical Application Circuit All Rights Reserved Copyright (C) Bee Technologies Corporation Filter & Load PWM Controller Power Switches  Schematic is captured from NJM2309 datasheet page 4.

All Rights Reserved Copyright (C) Bee Technologies Corporation ? 3? 4? 5? TASK: Design and Evaluation of the Circuit NJM2309 Typical Application Circuit

Buck Regulator Design Workflow All Rights Reserved Copyright (C) Bee Technologies Corporation Setting PWM Controller’s Parameters: VREF, VP 1 1 Setting Output Voltage: Rupper, Rlower 2 2 Inductor Selection: L 3 3 Capacitor Selection: C, ESR 4 4 Stabilizing the Converter: R2, C1, C2 Step1: Open the loop with LoL=1kH and CoL=1kF then inject an AC signal to generate Bode plot. (always default) Step2: Set C1=1kF, C2=1fF, (always keep the default value) and R2= calculated value (Rupper//Rlower) as the initial values. Step3: Select a crossover frequency (about 10kHz or fc < fosc/4). Then complete the table. Step4: Read the Gain and Phase value at the crossover frequency (10kHz) from the Bode plot, Then put the values to the table Step5: Select the phase margin at the fc ( > 45  ). Then change the K value until it gives the satisfied phase margin, for this example K=6 is chosen for Phase margin = 46 . Remark: If K-factor fail to gives the satisfied phase margin, Increase the output capacitor C then try Step1 to Step5 again. Load Transient Response Simulation

Buck Regulator Design Workflow All Rights Reserved Copyright (C) Bee Technologies Corporation

VREF = V B = 0.52 (V) VP=2.5 (v FBH and v FBL are not provided, the default value is used). Setting PWM Controller’s Parameters All Rights Reserved Copyright (C) Bee Technologies Corporation  Table is captured from NJM2309 datasheet page

Use the following formula to select the resistor values. R lower can be between 1k and 5k. Given: V OUT = 3.3V V REF = 0.52V R lower = 1k  then: R upper = 5.346k  Setting Output Voltage: Rupper, Rlower All Rights Reserved Copyright (C) Bee Technologies Corporation

Inductor Selection: L All Rights Reserved Copyright (C) Bee Technologies Corporation Inductor Value from Given: V I,max = 40(V), V OUT = 3.3(V) I OUT,min = 0.2(A) R L,min = (V OUT / I OUT,min ) = 16.5(  ) f osc = 105(kHz) Then: L CCM  72.1(uH), L = 100(uH) is selected 3 3

Capacitor Selection: C, ESR (NJM2309) All Rights Reserved Copyright (C) Bee Technologies Corporation Capacitor Value From and Given: V I, max = 40 V V OUT = 3.3 V, V OUT, Ripple = 1% ( 33mV P-P ) L (  H ) = 100 I OUT, MAX = 1(A), I L, Ripple = 0.25(A) Then: C  944 (  F ), C = 1000(  F ) is selected In addition: ESR  132m  4 4

Stabilizing the Converter (NJM2309) All Rights Reserved Copyright (C) Bee Technologies Corporation Specification: V OUT = 3.3V V IN = 6 ~ 32V I LOAD = 0.2 ~ 1A PWM Controller: VREF = 0.52V VP = 2.5V f OSC = 105kHz R lower = 1k , R upper = 5.346k , L = 100uH, C = 1000uF (ESR = 132m  ) Task: to find out the element of the Type 2 compensator ( R2, C1, and C2 ) G(s) e.g. Given values from National Semiconductor Corp. IC: LM

All Rights Reserved Copyright (C) Bee Technologies Corporation Step2 Set C1=1kF, C2=1fF, and R2=calculated value (R upper //R lower ) as the initial values. Step1 Open the loop with LoL=1kH and CoL=1kF then inject an AC signal to generate Bode plot. The element of the Type 2 compensator ( R2, C1, and C2 ), that stabilize the converter, can be extracted by using Type 2 Compensator Calculator (Excel sheet) and open-loop simulation with the Average Switch Models (ac models). Stabilizing the Converter (NJM2309) 5 5  C1=1kF is AC shorted, and C2 1fF is AC opened (or Error-Amp without compensator).

Stabilizing the Converter (NJM2309) Type 2 Compensator Calculator Switching frequency, fosc :105.00kHz Cross-over frequency, fc (<fosc/4) :10.00kHz Rupper :5.346kOhm Rlower :1kOhm R2 (Rupper//Rlower) :0.842kOhm(automatically calculated) PWM Vref :0.520V Vp  (Approximate) :2.5V All Rights Reserved Copyright (C) Bee Technologies Corporation Step3 Select a crossover frequency (about 10kHz or fc < fosc/4 ), for this example, 10kHz is selected. Then complete the table. Calculated value of the Rupper//Rlower values from

Parameter extracted from simulation Set: R2=R1, C1=1k, C2=1f Gain (PWM) at foc ( - or + ) : Phase (PWM) at foc : All Rights Reserved Copyright (C) Bee Technologies Corporation Step4 Read the Gain and Phase value at the crossover frequency (10kHz) from the Bode plot, Then put the values to the table. Stabilizing the Converter (NJM2309) Tip: To bring cursor to the fc = 10kHz type “ sfxv(10k) ” in Search Command. Cursor Search Gain: T(s) = H(s)  G PWM Phase  at fc 5 5

K-factor  (Choose K and from the table) K3  -217  (automatically calculated) Phase margin :48(automatically calculated) R2 :54.655kOhm(automatically calculated) C1 :0.847nFnF(automatically calculated) C2 :97.07pFpF(automatically calculated) Stabilizing the Converter (NJM2309) All Rights Reserved Copyright (C) Bee Technologies Corporation Step5 Select the phase margin at fc (> 45  ). Then change the K value (start from K=2) until it gives the satisfied phase margin, for this example K=3 is chosen for Phase margin = 48 . As the result; R2, C1, and C2 are calculated.  K Factor enable the circuit designer to choose a loop cross-over frequency and phase margin, and then determine the necessary component values to achieve these results. A very big K value (e.g. K > 100) acts like no compensator (C1 is shorted and C2 is opened). 5 5 Remark: If K-factor fail to gives the satisfied phase margin, Increase the output capacitor C then try Step1 to Step5 again.

Stabilizing the Converter (NJM2309) All Rights Reserved Copyright (C) Bee Technologies Corporation The element of the Type 2 compensator ( R2, C1, and C2 ) extraction can be completed by Type 2 Compensator Calculator (Excel sheet) with the converter average models (ac models) and open-loop simulation. The calculated values of the type 2 elements are: R2= k, C1= nF, C2= pF. The calculated values of the type 2 elements are: R2= k, C1= nF, C2= pF. *Analysis directives:.AC DEC MEG 5 5

Phase margin = at the cross-over frequency - fc = 9.237kHz. All Rights Reserved Copyright (C) Bee Technologies Corporation Stabilizing the Converter (NJM2309) Tip: To bring cursor to the cross-over point ( gain = 0dB) type “ sfle(0) ” in Search Command. Cursor Search Gain: T(s) = H(s)  G(s)  G PWM Phase  at fc 5 5 Gain and Phase responses after stabilizing

Load Transient Response Simulation All Rights Reserved Copyright (C) Bee Technologies Corporation The converter, that have been stabilized, are connected with step-load to perform load transient response simulation. 3.3V/16.5  = 0.2A step to =1.0A load *Analysis directives:.TRAN 0 20ms 0 1u

All Rights Reserved Copyright (C) Bee Technologies Corporation Output Voltage Change Load Current The simulation results illustrates the transient response of the converter with the stepping load.2A to 1A. Load Transient Response Simulation Simulation

Reference: Load Transient Response Simulation with PWM IC Transient Model All Rights Reserved Copyright (C) Bee Technologies Corporation After the converter have been designed, the PWM IC Transient Model could be applied for more realistic simulation. 3.3V/16.5  = 0.2A step to =1.0A load *Analysis directives:.TRAN 0 12ms 0 200n SKIPBP  Remark: PWM IC Transient Model and Simulations are not included with this package.

The PWM IC Transient Model enables The V OUT, RIPPLE and others switching characteristics to be included in the simulation. All Rights Reserved Copyright (C) Bee Technologies Corporation Output Voltage Change Load Current Simulation  Remark: PWM IC Transient Model and Simulations are not included with this package. Reference: Load Transient Response Simulation with PWM IC Transient Model

A. Type 2 Compensation Calculation using Excel Switching frequency, fosc : kHzGiven spec, datasheet Cross-over frequency, fc (<fosc/4) : kHzInput the chosen value ( about 10kHz or < fosc/4 ) Rupper : kOhmGiven spec, datasheet, or calculated Rlower : 1 kOhmGiven spec, datasheet, or value: 1k-10k Ohm R2 (Rupper//Rlower) : kOhm(automatically calculated) PWM Vref : VGiven spec, datasheet Vp (Approximate) : 2.5 VGiven spec, or calculated, (or leave default 2.5V) Parameter extracted from simulation Set: R2=R2, C1=1k, C2=1f Gain (PWM) at foc ( - or + ) : dBRead from simulation result Phase (PWM) at foc :  Read from simulation result K-factor (Choos K and  from the table) K 3 Input the chosen value (start from k=2)  -217  (automatically calculated) Phase margin : 48 (automatically calculated) Target value > 45 R2 : kOhm(automatically calculated) C1 : nFnF(automatically calculated) C2 : pFpF(automatically calculated) All Rights Reserved Copyright (C) Bee Technologies Corporation

All Rights Reserved Copyright (C) Bee Technologies Corporation B. Feedback Loop Compensators Type1 Compensator Type2 Compensator Type2a Compensator Type2b Compensator Type3 Compensator

All Rights Reserved Copyright (C) Bee Technologies Corporation SimulationsFolder name 1.Stabilizing the Converter Load Transient Response ac stepload Libraries : 1...\bucksw.lib 2...\pwm_ctr.lib Tool : Type 2 Compensator Calculator (Excel sheet) C. Simulation Index