Mixed Signal Products SLOA021A IMPORTANT NOTICE Texas Instru

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Current Feedback Amplifier Analysis Compensation
Mixed Signal Products
SLOA021A
IMPORTANT NOTICE Texas Instruments subsidiaries (TI) reserve right make changes their products discontinue product service without notice, advise customers obtain latest version relevant information verify, before placing orders, that information being relied current complete. products sold subject terms conditions sale supplied time order acknowledgment, including those pertaining warranty, patent infringement, limitation liability. warrants performance products specifications applicable time sale accordance with TI's standard warranty. Testing other quality control techniques utilized extent deems necessary support this warranty. Specific testing parameters each device necessarily performed, except those mandated government requirements. Customers responsible their applications using components. order minimize risks associated with customer's applications, adequate design operating safeguards must provided customer minimize inherent procedural hazards. assumes liability applications assistance customer product design. does warrant represent that license, either express implied, granted under patent right, copyright, mask work right, other intellectual property right covering relating combination, machine, process which such products services might used. TI's publication information regarding third party's products services does constitute TI's approval, license, warranty endorsement thereof. Reproduction information data books data sheets permissible only reproduction without alteration accompanied associated warranties, conditions, limitations notices. Representation reproduction this information with alteration voids warranties provided associated product service, unfair deceptive business practice, responsible liable such use. Resale TI's products services with statements different from beyond parameters stated that product service voids express implied warranties associated product service, unfair deceptive business practice, responsible liable such use. Also see: Standard Terms Conditions Sale Semiconductor Products. www.ti.com/sc/docs/stdterms.htm
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Contents
Introduction Model Development Stability Equation Noninverting Inverting Stability Analysis Selection Feedback Resistor Stability Input Capacitance Stability Feedback Capacitance Compensation CFAs Versus VFAs Summary
List Figures
Current Feedback Amplifier Model Stability Analysis Circuit Stability Analysis Schematic Noninverting Inverting Bode Plot Stability Equation Plot Effects Stray Capacitance CFAs Bode Plot with Feedback Capacitor
List Tables
Tabulation Pertinent Equations
Current Feedback Amplifier Analysis Compensation
SLOA021A
Current Feedback Amplifier Analysis Compensation
Mancini
ABSTRACT Current-feedback amplifiers have ideal closed-loop gain equations identical voltage-feedback amplifiers, similarity ends there. detailed gain equations current feedback amplifier developed here inverting noninverting circuits. This paper goes beyond gain analysis develops stability criteria discusses compensation.
Introduction
Current-feedback amplifiers (CFA) have traditional differential amplifier input structure, thus, they sacrifice parameter matching inherent that structure. circuit configuration prevents them from obtaining precision voltage-feedback amplifiers (VFA), circuit configuration that sacrifices precision results increased bandwidth slew rate. higher bandwidth relatively independent closed-loop gain, constant gain-bandwidth restriction applied VFAs removed CFAs. slew rate CFAs much improved from their counterpart VFAs because their structure enables output stage supply slewing current until output reaches final value. general, VFAs used precision general purpose applications, while CFAs restricted high frequency applications above MHz. Although CFAs have precision their counterparts, they precise enough dc-coupled video applications where dynamic range requirements severe. CFAs, unlike previous generation high-frequency amplifiers, have eliminated ac-coupling requirement; they usually dc-coupled while they operate range. CFAs have much faster slew rates than VFAs, they have faster rise/fall times less intermodulation distortion. This application note assumes that reader familiar with feedback electronics VFAs. Refer Texas Instruments application note SLVA058 basic feedback analysis tools. Texas Instruments application note SLOA020 covers stability theory.
Model
model shown Figure noninverting input connects input buffer (input buffer), very high impedance similar bipolar transistor input. inverting input connects input buffer's output, inverting input impedance very low. models input buffer's output impedance, usually less than buffer gain (GB) close design methods achieve, neglected calculations.
Development Stability Equation
NONINVERTING INPUT
Z(I) ZOUT GOUT VOUT
INVERTING INPUT
Figure Current Feedback Amplifier Model output buffer provides output impedance amplifier. Again, output-buffer gain (GOUT) very close one, neglected this analysis. output impedance output buffer ignored except when driving very impedance capacitive loads. input buffer's output impedance ignored because affects stability high frequencies. current-controlled current source (ZI) transimpedance. transimpedance serves same function gain VFA; parameter that makes performance dependent only passive parameter values. Usually transimpedance very high, megohm range, obtains accuracy closing feedback loop manner similar VFA.
Development Stability Equation
stability equation developed with Figure Remember, stability independent input, stability depends solely loop gain (A). stability equation developed breaking loop point inserting test signal (VTI), calculating return signal (VTO). circuit shown Figure model substituted symbol. input-buffer gain, output-buffer gain, output-buffer output impedance have been left circuit simplify calculations. This approximation valid almost applications.
VOUT Becomes VTO; Test Signal Output Break Loop Here Apply Test Signal (VTI) Here
Figure Stability Analysis Circuit
VOUT
Figure Stability Analysis Schematic
SLOA021A
Noninverting
transfer equation given equation Kirchoff's used write equations
Equations combined yield equation
Dividing equation equation yields equation which open-loop transfer equation. This equation commonly known loop gain.
Noninverting
closed-loop gain equation noninverting developed with Figure where external gain setting resistors have been added. buffers shown Figure because their gains equal they included feedback loop, they enter into calculations.
VOUT
Figure Noninverting Equation transfer equation, equation current equation inverting node, equation input-loop equation. These equations combined yield equation closed-loop gain equation.
Current Feedback Amplifier Analysis Compensation
Inverting
When input buffer output impedance (ZB) approaches zero, equation reduces equation
(10)
When transimpedance (Z), very high term ZF/Z equation approaches zero, equation reduces equation which ideal closed-loop gain equation CFA. ideal closed-loop gain equations noninverting amps identical, degree which they depart from ideal dependent validity assumptions. assumption: direct gain very high, while assumptions: transimpedance very high input buffer output impedance very low. would expected, assumptions harder meet than one; thus departs from ideal more than does. +1)Z
(11)
Inverting
inverting configuration seldom used because input impedance very (ZB||ZF +ZG). When made dominant selecting high resistance value, overrides effect must also selected high value achieve least unity gain. High values result poor bandwidth performance seen next section. selected value (ZB) which frequency sensitive, causes gain increase frequency increases. These limitations restrict applications inverting CFA.
SLOA021A
Inverting
VOUT
Figure Inverting current equation input node written equation Equation defines dummy variable (VA) equation transfer equation CFA. These equations combined simplified leading equation which closed-loop gain equation inverting CFA.
(12) (13) (14)
(15)
When approaches zero, equation reduces equation
(16)
When very large, equation becomes equation which ideal closed-loop gain equation inverting CFA. (17)
Current Feedback Amplifier Analysis Compensation
Stability Analysis
ideal closed-loop gain equations inverting amps identical. Both configurations have lower input impedance than noninverting configuration has, assumption while assumptions. Again, case with noninverting counterparts, less ideal than because assumptions. zero assumption always breaks down bipolar-junction transistors, shown later. differential amplifier configuration almost never used with CFAs because gross input impedance mismatch.
Stability Analysis
stability equation repeated equation
(18)
Comparing equations equation shows that inverting noninverting amps have identical stability equations. This expected result because stability feedback circuit function loop gain, input signals have affect stability. parameters affecting stability transimpedance input buffer's output impedance (ZB). external components affecting stability external impedances controlled designer, although stray capacitance, which part external impedance, sometimes appears uncontrollable. Stray capacitance primary cause ringing overshoot CFAs. parameters, they cannot controlled circuit designer, designer must deal with them. Prior determining stability with Bode plot, take equation plot logs (equations Figure 20LOG|Ab|
TANGET
20LOG|Z|-20LOG
-1(A
(19)
(20)
plot, called Bode plot, named after Bode, first developed forties. enables designer subtract components stability equation graphically.
SLOA021A
Stability Analysis
AMPLITUDE
20LOGIZI 20LOGIZF(1 ZB/ZFIIZG)I
61.1 58.9 Composit Curve -120 -180 LOG(f)
PHASE (DEGREES)
Figure Bode Plot Stability Equation plot Figure assumes typical values parameters:
1MW)
(21) (22) (23)
transimpedance poles, plot shows that will unstable without addition external components because 20LOG|Z| crosses 0-dB axis after phase shift equals 180°. reduce loop gain 61.1 circuit stable because phase margin. Notice that parallel combination contribute little phase margin because small, have little effect stability. manufacturer determines optimum value during characterization Referring Figure seen that when exceeds optimum value recommended manufacturer, stability increases. increased stability price called decreased bandwidth. Conversely, when less than optimum value recommended manufacturer, stability decreases, circuit response step inputs overshoot possibly ringing. Sometimes overshoot associated with less than optimum tolerated because bandwidth increases decreases. peaked response associated with less than optimum values used compensate cable droop caused cable capacitance. When loop gain equation Z/RF. Under these conditions, stability determined value always found stabilize circuit. transimpedance feedback resistor have major impact stability, input buffer's output impedance minor effect stability. Since increases with increase frequency, tends increase stability higher frequencies. Equation rewritten equation been manipulated that ideal closed-loop gain readily apparent.
(24)
Current Feedback Amplifier Analysis Compensation
Selection Feedback Resistor
important enough warrant further investigation, equation given equation
(25)
frequencies RB/(0+1) varies accordance with equation high frequencies. Also, transistor parameters equation vary with transistor type; they different transistors. Because dependent output transistors being used, this function quadrant output signal extremely wide variation. small factor equation, adds variability current feedback amp.
Selection Feedback Resistor
feedback resistor determines stability, effect closed-loop bandwidth, must selected very carefully. Most manufacturers employ applications product engineers spend great deal time effort selecting They measure each closed-loop gain with several different feedback resistor values gather data. Then they pick compromise value that yields stable operation with peaking, that value recommended data sheet that specific gain. This procedure repeated several different gains anticipation various gains their customer applications require (often When value gain changed from values recommended data sheet, bandwidth and/or stability affected. When circuit designer must select different value from that recommended data sheet gets into stability low-bandwidth problems. Lowering decreases stability, increasing decreases bandwidth. What happens when designer needs operate gain specified data sheet? designer must select value gain, there guarantee that value optimum value. solution selection problem assume that loop gain, linear function. Then assumption made that (A)1 gain equals (A)N gain that this linear relationship between stability gain. Equations based linearity assumption.
(26)
(27)
SLOA021A
Stability Input Capacitance
Equation leads believe that value easily chosen each gain. This case real world; assumptions don't hold well enough rely them. When change gain specified data sheet, equation best, supplies starting point must test determine final value When value recommended data sheet can't used, alternate method selecting starting value graphical techniques. graph shown Figure plot typical 300-MHz data given Table
GAIN BANDWIDTH FEEDBACK RESISTOR
Gain
Bandwidth Feedback Resistance Gain Feedback Resistance
Bandwidth
Feedback Resistor
Figure Plot
Stability Input Capacitance
When stray capacitance forms inverting input node ground, causes impedance become reactive. impedance (ZG) given equation equation stability equation that describes situation.
(28)
(29)
(30)
Current Feedback Amplifier Analysis Compensation
Stability Feedback Capacitance
Equation stability equation when consists resistor parallel with stray capacitance between inverting input node ground. stray capacitance, fixed value because dependent circuit layout. pole created stray capacitance dependent because dominates fluctuates with manufacturing tolerances, RBCG pole placement subject manufacturing tolerances. RBCG combination becomes larger, pole moves towards zero frequency axis, lowering circuit stability. Eventually interacts with pole contained 1/2, instability results. effects stray capacitance closed-loop performance shown Figure
AMPLITUDE FREQUENCY
Amplitude dB/div)
Stray Capacitance
Frequency
Figure Effects Stray Capacitance CFAs Notice that introduction causes more than 3-dB peaking frequency response plot, increases bandwidth about MHz. picofarads capacitance because sloppy layout easily more picofarads circuit.
Stability Feedback Capacitance
When stray capacitor formed across feedback resistor, feedback impedance given equation Equation gives loop gain when feedback capacitor been added circuit.
(31)
SLOA021A
Compensation
(32)
This loop-gain transfer function contains pole zero, thus, depending pole/zero placement, oscillation result. Bode plot this case shown Figure original composite curves cross 0-dB axis with slope dB/decade, either curve indicate instability. composite curve crosses 0-dB axis higher frequency than original curve; hence, stray capacitance added more phase shift system. composite curve surely less stable than original curve. Adding capacitance inverting input node across feedback resistor usually results instability. largely influences location pole introduced thus, here another case where stray capacitance leads instability. Figure shows that adds about peaking frequency response plot. bandwidth increases about because peaking. major causes overshoot, ringing, oscillation CFAs, circuit board layout must carefully done eliminate these stray capacitances.
20LOGIZI 20LOGIZF(1 ZB/ZFIIZG)I AMPLITUDE
POLE/ZERO Curve
Composit Curve
LOG(f)
Figure Bode Plot with Feedback Capacitor
Compensation
When both present circuit, they adjusted cancel each other out. stability equation equation
(33)
zero pole equation cancel each other, only poles remaining Setting pole zero equation equal yields equation after some algebraic manipulation.
Current Feedback Amplifier Analysis Compensation
(34)
CFAs Versus VFAs
dominates parallel combination equation reduced equation
(35)
parameter, dependent process. important parameter, important enough monitored control variable during manufacturing process. widely spread, unspecified parameters, depending compensation risky. Rather, product design engineer assumes that circuit will stable reasonable value that resulting frequency response peaking acceptable.
CFAs Versus VFAs
equations given Table closed-loop gain both amps identical, remaining equations different. This situation leads natural conclusion that ideal closed-loop performance identical long approximations remain true. approximations true frequencies much lower than advertised -3-dB frequency, they fall apart -3-dB frequency. Both types amps have particular niche markets. VFAs dominate precision low-voltage/low-power markets. VFAs dominate precision market because their differential amplifier input structure enables them employ matching eliminate offset voltages currents. VFAs dominant low-voltage/power market because their circuit configuration enables them operate rail-to-rail mode. VFAs have poor slew rate, this limits their pulse handling capability. CFAs have much higher bandwidth because have much lower impedances inverting input circuit feedback circuit. bandwidth stays high longer CFAs; thus, 50-MHz usable much higher frequencies than 50-MHz VFA. circuit topology enables them supply slew current from output structure, thus, they have much faster slew rates. CFAs stability determined value feedback resistor. Table Tabulation Pertinent Equations
CIRCUIT CONFIGURATION NONINVERTING Direct gain CURRENT FEEDBACK AMPLIFIER VOLTAGE FEEDBACK AMPLIFIER
Loop gain Closed-loop gain INVERTING Direct gain Loop gain Closed-loop gain
SLOA021A
Summary
Summary
limited constant gain-bandwidth criteria, feedback resistor adjusted maximum performance. stability dependent feedback resistor; decreased stability decreased, when goes zero, circuit becomes unstable. increased stability increases, bandwidth decreases. noninverting input impedance very high, inverting input impedance very low. This situation precludes CFAs from operation differential amplifier configuration. Stray capacitance inverting input node across feedback resistor always leads peaking, usually ringing, sometimes oscillations. prudent circuit designer scans board layout stray capacitances eliminates them. Breadboarding testing necessary with CFAs. performance improved immeasurably with good layout, good decoupling capacitors, low-inductance components.
Current Feedback Amplifier Analysis Compensation

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