Conversion Using bq2031 bq2031 incorporates necessary control cir

The Datasheet Archive - 100 Million Datasheets from 7500 Manufacturers.

Conversion Using bq2031 bq2031 incorporates necessary control cir

Datasheet Thumbnail

Top Searches for this datasheet

Switch-Mode Power
Conversion Using bq2031
bq2031 incorporates necessary control circuitry support switch-mode voltage current regulation, required charge control function block. This application note describes configure bq2031 buck mode switching power supply topology. methodology phase compensation voltage current feedback loops recommended. brief description control circuitry phase compensation criteria appears below, followed discussion dealing with topology specific issues. relationship CPWM switching frequency, given Equation where: CPWM either loop consists comparator whose positive terminal driven output sawtooth ramp signal, while negative terminal driven output Operational Transconductance Amplifier (OTA). output control signal, output each logically ORed generate constant frequency pulse width modulated rectangular waveform output. relationship output with respect control signal, sawtooth ramp signal, shown Figure
CPWM
Pulse Width Modulator
bq2031 incorporates voltage mode direct duty cycle Pulse Width Modulators, each control loop (voltage current). block diagram shown Figure Each runs common saw-tooth waveform whose time-base controlled capacitor, CPWM TPWM pin.
Figure Block Diagram bq2031 Control Circuitry
June 1996
Switch-Mode Power Conversion Using bq2031 output swings rail-to-rail source sink 10mA. used control switching transistor switch-mode application. pulse width modulated square wave signal synchronized internal sawtooth ramp signal. ramp-down time (TD) fixed approximately total period (TP). This condition limits maximum duty-cycle approximately 80%. example, with switching frequency 100kHz, 2µs.
Voltage Current Control Loops
independent function blocks implement direct duty cycle control current voltage regulation. During current regulation feedback signal voltage across current sense resistor, RSNS, shown current feedback loop model Figure current regulation total open-loop transfer function, IL(s), expressed Equation IL(s) A(s) P(s) PT(s) where: A(s) error amplifier compensation network transfer function, VC/VO P(s) transfer function, D/VC PT(s) power train transfer function, VO/D duty cycle waveform
Phase Compensation
feedback control system, phase compensation necessary achieve both loop stability dynamic line load response. shown block diagram (Figure bq2031 provides high-impedance nodes, ICOMP VCOMP, current voltage loop phase compensation. battery charger application dynamic load response much concern loop stability, especially during voltage regulation.
Figure Relationship Output Sawtooth Waveform Control Signal
June 1996
Preliminary Switch-Mode Power Conversion Using bq2031
During voltage regulation, feedback signal voltage sensed midpoint battery voltage divider (between RB2). voltage feedback control loop modeled shown Figure
Figure Model Current Control Loop
Figure Model Voltage Control Loop
June 1996
Switch-Mode Power Conversion Using bq2031 voltage regulation, total open-loop transfer function, VL(s), expressed Equation VL(s) A(s) P(s) PT(s) where: PT(s) transfer function output power stage, VO/D. switching frequency circuit topology system dictate gain-frequency characteristics output power stage. characteristics fixed within bq2031. This situation leaves associated compensation network only function block whose characteristics changed achieve desired loop stability response. where: DMAX maximum duty cycle waveform peak-to-peak amplitude sawtooth waveform bq2031, fixed 1.7V, maximum duty cycle 80%. This condition reduces transfer function Equation P(s) 0.47 PT(s) (the transfer function output power stage) given Equation PT(s) RSNS P(s) (the transfer function PWM) given P(s) DMAX
Error Amplifier
bq2031 error amplifiers (Operational Transconductance Amplifier) type. parameters interest (see Figure are: Transconductance gain, 0.42 milli-mhos Output resistance error amplifier, 250k Gain Bandwidth product 80MHz This situation fixes maximum voltage gain (gm*R) 40.4dB, which good corner frequency 2MHz. Note that 40dB gain maximum achievable, regardless impedance across output ground.
RSNS RORL RSNS
where: complex variable input voltage equivalent internal battery capacitance (see Figure inductor value inductor resistance equivalent internal battery resistance (see Figure RSNS sense resistor value equivalent battery load resistance (see Figure Stabilizing current loop requires compensation loop error amplifier such that transfer function A(s) dominant pole characteristics. This achieved adding capacitor, between ground output error amplier shown Figure transfer function A(s) given
Criteria Loop Stability
gain phase characteristics associated circuitry must adjusted meet following three criteria loop stability: Total open-loop gain (IL(s) VL(s) above) must forced crossover frequency (FC) equal least switching frequency (FS). phase total open-loop gain must least degress less than degrees.
above criteria loop stability easily achieved total loop-gain transfer function exhibits dominant pole characteristics shown Figure
Stabilizing Current Loop
From Equation total open-loop transfer function expressed IL(s) A(s) P(s) PT(s)
A(s)
Ci))
June 1996
Preliminary Switch-Mode Power Conversion Using bq2031
Dominant Pole
Gain (dB)
Crossover Frequency
10^4 10^5 10^6
Switching Frequency
10^3
frequency (Hz)
phase (deg.)
-100 10^3 10^4 10^5 10^6
frequency (Hz)
Figure Target Gain Phase Characteristics Stable Closed-Loop System
June 1996
Switch-Mode Power Conversion Using bq2031 Substituting values get: Equation resultant transfer function compensated error amplifier expressed Equation
A(s)
where:
250000 Ci))
A(s)
where:
sRB1CF) CV)) sDRB1CF) s(2.5105
output capacitance error amplifier (see Figure Substituting Equations Equation gives compensated total current loop gain transfer function: Equation IL(s)
Battery voltage divider ratio during voltage regulation: ((RB2 RB3) RB1)
0.47 250000 Ci))
shown bode plot IL(s) (Figure varied achieve necessary phase gain margin different values.
Note: application note entitled "Using bq2031 Charge Lead-Acid Batteries" instructions calculating RB1, RB2, RB3.
Stabilizing Voltage Loop
Recalling Equation voltage regulation open-loop transfer function expressed VL(s) A(s) P(s) PT(s) output power stage transfer function PT(s) depends inductor battery impedances. components required compensate error amplifier achieving voltage loop stability appear Figure
resistor value between high side battery stack battery voltage divider network capacitance parallel with series resistance between VCOMP ground series capacitance between VCOMP ground (see Figure Voltage Loop Error Amplifier Compensation below calculating values CV.) above transfer function contributes poles zeros.
Figure Compensation Network Current Loop
June 1996
Preliminary Switch-Mode Power Conversion Using bq2031
phase (deg.)
-100 10^3 10^4 10^5 10^6
frequency (Hz)
Gain (dB)
-100 10^3 10^4 10^5 10^6
frequency (Hz)
Figure Bode Plot Current Loop-Gain Transfer Function
June 1996
Switch-Mode Power Conversion Using bq2031 Poles (Equation (2.5 compensated reference 0.275V. This turn regulates current IMAX, provided that properly designed resistor network use. passive component ICOMP VCOMP form phase compensation network current voltage control loops, respectively. diode (Db1) prevents battery drain when absent, while pull-up resistor detects battery removal. resistor R13, typically tens optional depends battery impedance resistance battery leads from charger board.
Zeroes (Equation
Output Power Stage
output power stage buck topology charger comprises inductor parallel combination output capacitor, impedance battery (see Figure 12). output capacitor electrolytic range from 47µF 100µF. nullifies inductive effect long leads from charger terminals battery.
effect this feedback compensation network transfer function A(s) shown Figure
Voltage Loop Compensation Buck Topology
Figure shows functional diagram switch-mode buck topology converter using bq2031. battery voltage divided down per-cell equivalent value pin. During voltage regulation, voltage (VBAT) regulated internal band-gap reference 2.2V (with temperature drift -3.9mV/°C). charge current through inductor sensed across resistor RSNS. During current regulation, bq2031 regulates voltage (VSNS) temperature-
Inductor Selection
inductor selection criteria DC-DC buck converter vary depending charging algorithm used. Two-Step Current Pulsed Current charge algorithms, inductor equation
Figure Compensation Network Voltage Loop
June 1996
Preliminary Switch-Mode Power Conversion Using bq2031
phase (deg.)
10^3
10^4
10^5
10^6
frequency (Hz)
Gain (dB)
10^3
10^4
10^5
10^6
frequency (Hz)
Figure Effect Compensation Network Amplifier Transfer Function, A(s)
June 1996
Switch-Mode Power Conversion Using bq2031
Figure Functional Diagram Switch-Mode Buck Regulator Lead-Acid Charger Using bq2031
June 1996
Preliminary Switch-Mode Power Conversion Using bq2031
Equation where: number cells VBLK bulk voltage cell, volts switching frequency, hertz ripple current IMAX, amps ripple current usually between 20-25% IMAX. Example: 6-cell battery charged IMAX 2.75A buck topology running 100kHz. VBLK threshold 2.45V cell charger configured Pulsed Current mode. Assuming ripple IMAX, inductor value required 2.45 0.5) (105 0.6875) 107µH VBLK 0.5) figured Two-Step Voltage mode, with IMIN IMAX/20. inductor value required 2.45 (105 0.1375) 267µH
Model Lead Acid Battery
battery impedance represented capacitor (CB) series with internal impedance shown Figure capacitance empirically derived from amp-hour rating battery. rule thumb where capacity battery ampere-hours. internal resistance lead-acid battery dictated Number cells, Amp-hour capacity, State charge Figure shows variation internal impedance Yuasa NP6-12 (12V, amp-hrs) battery function state charge. average value impedance swing recommended loop stability equations. example, with battery above recommend using 0.05. resistor models loading effects battery when voltage equivalent VBLK (typically 2.45V/cell) applied across battery. range values takes depends bulk charge current, bulk voltage, IMIN IMAX ratio. example:
inductor current, which must remain continuous down IMIN during Fast Charge phase (voltage regulation phase), dictates inductor formula TwoStep Voltage charge algorithm. Equation VBLK IMIN
Example: 6-cell battery charged IMAX 2.75A buck topology running kHz. VBLK threshold 2.45V cell charger con-
Figure Model Output Filter Buck Topology
June 1996
Switch-Mode Power Conversion Using bq2031 battery being charged IMAX will exhibit following range with IMIN/IMAX ratio 1:20. RL(min) RL(max) second pole used these calculations:
2.45
0.15
2.45
(RiCB L/RO)
Typical Switch-Mode Buck Charger Specifications
application specifications switch-mode buck topology charger usually given input voltage, Switching frequency, 100kHz, 10µs Charge algorithm Two-Step Voltage mode:
minimum value worst case scenario loop stability.
Power Stage Transfer Function
transfer function output power stage, PT(s) expressed Equation PT(s) where: CB))
(RiCB L/RO)))
VBLK 2.45V/cell Vflt 2.2V/cell IMAX IMIN IMAX/30 300mA
Battery specs: 12V, 10A-hr, Internal impedance: 0.02 0.07
poles zeros PT(s) are: Equation
Output Power Stage Transfer Functions
Starting again from basic voltage regulation loopgain transfer function (Equation given
Internal Battery Resistance
Internal Resistance Terminal Voltage
1.53A 1.02A 10HR 560mA 20HR 300mA
Discharge Time (Hours)
Figure Internal Resistance Yuasa NP6-12 Battery State Charge
June 1996
Preliminary Switch-Mode Power Conversion Using bq2031
VL(s) A(s) P(s) PT(s) This equation written VL(s) A(s) G(s) where G(s) combined transfer function P(s) PT(s) Combining Equations Equation zeros A(s), fz2, cancel second order poles G(s) fpo: fpo/2 263/2 131.5 From Equation 10's first zero, fz1: 4.63nF fz1) 2.61 131)
From Equation second pole, fp2: 0.47 CB)) (RiCB L/RO))) fp2= order achieve loop-gain compensated amplifier gain must forced absolute gain G(s) crossover frequency, which determined from Bode plot Figure -31dB 35.48. value determined from gain magnitude equation A(s) (fp2)
G(s)
Based typical values section above, worst case values loop parameters are: 0.05 1000µF From Equation 2.45 0.5) (105 0.1) 367.5µH
Using value 35.48 A(fp2) above equation gives: 35.48 450k 35.48 15.75
resulting bode plots G(s) shown below. Since plots exhibit similar characteristics that output power filter, Equation determine poles zeros: 263Hz 3183Hz
Plugging this value into equation yields:
2.7nF
Substituting these values equation gives: (450k (2.5 105)) 2.7nF 84.2Hz
Voltage Loop Error Amplifier Compensation
this control loop, must find appropriate values compensation components VCOMP pin. From Table "Using bq2031 Charge Lead-Acid Batteries" values divider network components are: RB1=261K RB2=49.9K RB3= 475K Therefore (RB2 RB3) 0.15 (RB2 (RB1 (RB2 RB3)))
Figures show resultant Bode loop gain plots A(s), respectively.
Current Loop Error Amplifier Compensation
this control loop, must find value compensation component ICOMP pin. compensation network component must chosen such that current loop gain transfer function dominant pole 1/20th switching frequency, F(s).
(2.5 105)
131.5 4.84nF
From first criterion loop stability, crossover frequency loop-gain) 1/20th switching frequency: FS/20 5kHz
(2.5 105) 131.5
June 1996
Switch-Mode Power Conversion Using bq2031
phase (deg.)
-120 10^3 10^4 10^5 10^6
frequency (Hz)
Gain (dB)
10^3
10^4
10^5
10^6
frequency (Hz)
Figure Bode Plot G(s)
June 1996
Preliminary Switch-Mode Power Conversion Using bq2031
phase (deg.)
10^3
10^4
10^5
10^6
frequency (Hz)
Gain (dB)
10^3
10^4
10^5
10^6
frequency (Hz)
Figure Bode Plot Error Amplifier, A(s)
June 1996
Switch-Mode Power Conversion Using bq2031
phase (deg.)
-100
10^3
10^4
10^5
10^6
frequency (Hz)
Gain (dB)
10^3
10^4
10^5
10^6
frequency (Hz)
Figure Loop Gain Bode/Example Buck Charger Design
June 1996

Conversion Using bq2031 bq2031 incorporates necessary control cir

Top Searches for this datasheet

Other recent searches