Apex Voltage to Current Conversion

8/13/2019 Apex Voltage to Current Conversion

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AN13 Voltage toCurrent Conversion

VOLTAGE TO CURRENT CONVERSION

Voltage controlled current sources (or VCCSs) can be useful

for applications such as active loads for use in component testingor torque control for motors. Torque control is simplied sincetorque is a direct function of current in a motor. Current drivein servo loops reduces the phase lag due to motor inductanceand simplies stabilizing of the loop.

VCCSs using power op amps will assume one of twobasic forms, depending on whether or not the load needs tobe grounded.

CURRENT SOURCE: FLOATING LOAD

Figure 1A illustrates the basic circuit of a VCCS for a oat-ing load. The load is actually in the feedback path. R S is acurrent sense resistor that develops a voltage proportional toload current.

Note the inclusion of resistor R B in Figure 1A and subsequentgures where non-inverting VCCSs are described. This resis-tor is present to prevent the non-inverting input from oatingwhen the input voltage source is disconnected or goes to highimpedance during the power on cycle. R B provides a path forinput bias current of the amplier and commands the amplieroutput current to zero in cases where V IN is disconnected orgoes to a high impedance. Figure 1B shows an implementationof a VCCS for a oating load. At low frequencies the addedcomponents Cf, Rd, and R F have no effect and are includedonly to insure stability. Considerations for these componentsare discussed in the section on Stabilizing the Floating LoadVCCS covered later in this application note.

The ampliers loop gain will force the voltage across R S toassume a value equal to the voltage applied to the non-invertinginput, resulting in a transfer function of:

IO=VIN /R S

LOAD

+V S

V SR BV IN

R S

FIGURE 1A. BASIC VCCS FOR FLOATING LOAD

Several variations are possible for this basic circuit. It is notnecessary to have a direct feedback connection from R S tothe inverting input; components can be included to raise thegain of the circuit. Figure 2 shows a higher gain version withits equivalent transfer function. Higher gain circuits will losesome accuracy and bandwidth, but can be easier to stabilize.

Figure 3 shows an inverting VCCS. The input voltage resultsin an opposite polarity of current output. Just as in the caseof inverting voltage ampliers, the advantage of not havingany common mode variation at the amplier input is higheraccuracy and lower distortion.

Figure 4 is a current input version which is actually a CCCS,or current controlled current source. This is truly a currentamplier. This circuit could be useful with current output Digital-to-Analog Converters (DACs), or in any application where acurrent is available as an input.

LOAD

+V S

V SR BV IN

R S

I O

RdCf

R F

I O =V IN

R S

FIGURE 1B. VCCS FOR FLOATING LOAD WITH STABILITY COMPENSATION

LOAD

+VS

VSR BV IN

R S

I O

RdCf

R F

I O =V INR S

(1 + )R FR I

FOR: R


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STABILIZING THE FLOATING LOAD VCCS

Because the load is in the feedback loop on all of thesecircuits, it will have a signicant effect on stability. If the loadwas always purely resistive, the analysis would be simple andmany circuits would not require any additional components(such as Cf and Rd) to insure stability. In the real world however,we usually nd ourselves using these circuits to drive such

complex loads as magnetic coils and motors.Stability analysis is most easily accomplished using Rate of

Closure techniques where the response of the the feedback isplotted against the amplier open loop gain. This technique usesinformation easily obtained on any amplier data sheet.

Rate-of-closure refers to how the response of the feedbackand amplier Aol intersect. If the slope of the combined intersec-tion is not over 20 dB per decade, the circuit will be stable.

For an example, consider the amplier of Figure 1A. Assumea PA07 amplier with a 0.5 ohm current sense resistor will beused to drive a 50 H coil with 1 ohm of series resistance. InFigure 5 we have superimposed on the Aol graph of the PA07the response of the load and sense resistor.

The intersection of the responses exhibits a combined slopeof 40 dB per decade, leading to ringing or outright oscillation.Lets refer to that point as the critical intersection frequency.Compensation for this circuit is best accomplished with analternate feedback path; the response of which will dominateat the critical intersection frequency.

A good criteria for the response of the alternate feedbackwould be:1. A response which dominates by at least an order of mag-

nitude (20 dB) at the critical intersection frequency.2. The alternate feedback response should have a corner

occurring at a frequency an order of magnitude less thanthe critical intersection frequency.To provide this response, the alternate feedback components

have been selected to provide the compensating responseillustrated in Figure 6. A B in Figure 6 is the dominant feedbackpath the amplier will see in its closed loop conguration. R F merely acts as a ground leg return impedance for the alternatefeedback loop, and should be a low value between 100 and1000 ohms. Rd is then selected to provide the desired highfrequency gain, and Cf is selected for the alternate feedback

+VS

VSR BV IN

R S

PA07

100K

L L

R L

50H

1.0

0.5

120

100

80

60

40

20

0

201 10 100 1K 10K .1M 1M 10M

O P E N L O O P G A I N

, A ( d B )

FREQUENCY, F(Hz)

SMALL SIGNAL RESPONSE

40dB/decaderate ofclosure

FeedbackResponse(1/)

1/ DC Fz =R L+R S

2L L

FIGURE 5. PLOTTING FEEDBACK RESPONSES

DC =.5

1.5= .333 1/ = 9.5dB Fz = 1.0 + .5

2 50H= 4.77kHz

corner.Note that these are similar to techniques used to stabilize

magnetic deection ampliers described in Apex Microtechnol-ogy AN05, Precision Magnetic Deection.

CURRENT OUTPUT FOR GROUNDED LOAD

The VCCS for a grounded load is sometimes referred to asthe Improved Howland Current Pump. It is actually a dif-ferential amplier which senses both input signal and feedbackdifferentially.

Figure 7 shows a general example for this VCCS with itsassociated transfer function.

First among the special considerations for this circuit is thatthe two input resistors (R

I), and the two feedback resistors

(RF), must be closely matched. Even slight mismatching willcause large errors in the transfer function and degrade theoutput impedance causing the circuit to become less of a truecurrent source.

As an example of the matching requirement, consider theactual example using PA07 in Figure 8. Matching the resis-tors as closely as tolerances permitted produced an outputimpedance of 43 K ohms. A 1% mismatch reduced outputimpedance to 200 ohms and introduced nearly 20% error intothe transfer function.

This suggests that matching to better than 0.1% is requiredwhich is probably best accomplished with prepackaged resis-

+VS

VS

R BV IN

R S

PA07

100K

L L

R L

50H

1.0

0.5

120

100

80

60

40

20

0

201 10 100 1K 10K . 1M 1M 10M

O P E N L O O P G A I N

, A ( d B )

FREQUENCY, F(Hz)

SMALL SIGNAL RESPONSE

RdCf

FB #1

R F

100

332.047F

FB #2

FB #2

FB #1

A

FIGURE 6. COMPENSATING THE AMPLIFIER

I O =V IN

R S

R F

R I

FOR: R


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tor networks with excellent ratio match. The circuit of Figure8 actually required a slight amount of mismatch in the two(RF) resistors to compensate for mismatches elsewhere,suggesting that the inclusion of a trimpot may be necessaryto obtain maximum performance.

STABILITY WITH THE GROUNDED LOAD CIRCUIT

The grounded load circuit is remarkably forgiving from astability standpoint. Generally, no additional measures needto be taken to insure stability.

Any stability problems that do arise are likely to be a resultof the output impedance of the circuit appearing capacitive.The equivalent capacitance can be expressed as follows:

Where: fo = THE GAIN-BANDWIDTH PRODUCT OF THEAMPLIFIER

This capacitance can resonate with inductive loads, re-sulting most often in ringing problems with rapid transitions.The only effective compensation is a simple Q-snubber technique: determine the resonant frequency of the inductiveload and output capacitance of the circuit. Then, select aresistor value one-tenth the reactance of the inductor at theresonant frequency. Add a series capacitor with a reactanceat the resonant frequency equal to one-tenth of the resistorvalue. An alternate method would be to put a small inductorand damping resistor in series with R S .

Also keep in mind that the equation favors larger values ofR I and R S , and the use of op amps with better gain-bandwidthto reduce effective capacitance. In circuits where good highfrequency performance is required, this will necessitateincreasing either or both R I and R S with the upper limits be-ing established where stray capacitance and amplier inputcapacitance become signicant.

An infrequent second cause of instability in this circuit isdue to negative resistance in the output impedance charac-teristic of the circuit. This problem can be solved by trimming

the feedback resistors to improve matching.THE CURRENT MIRROR

The current mirror circuit is a handy device for generatinga second current that is proportional to input current but op-posite in direction.

The mirror in Figure 9 must be driven from a true currentsource in order to have exible voltage compliance at theinput. Any input current will attempt to develop a drop acrossR1 which will be matched by the drop across R2 causing thecurrent through R2 to be ratioed to that in R1. For example, ifR1 were 1.0 K ohm and R2 were 1 ohm, then 1 mA of input

current will produce 1 Amp of output current.

RATE-OF-CLOSURE AND FEEDBACK RESPONSE

Rate-of-closure stability analysis techniques are a methodof plotting feedback response against amplier response todetermine stability.

The closed loop gain of any feedback amplier is given by:Acl = Aol/(1-Aol)

Where: Aol IS THE OPEN-LOOP GAIN OF THE AMPLI-FIER, AND Acl IS THE RESULTANT CLOSEDLOOP GAIN

is a term describing the attenuation from the output signalto the signal fed back to the input (see Figure 10). In otherwords, is the ratio of voltage fed back to the amplier overthe ampliers output voltage. (Vfeedback=Vout)

In the examples used in this application note, the plottingof versus amplier response is facilitated by plotting anequivalent closed loop response (1/) of the amplier circuitand superimposing this response on the amplier open loopresponse. This equivalent closed loop response is alsoreferred to as noise gain, Av (n).

In the example in Figure 5, the curve referred to as feedbackresponse is actually representative of the closed loop noisegain response of the amplier due to the feedback networkconsisting of yoke and sense resistor. In Figure 6, an additionalfeedback response for Cf, Rd, and R F is plotted independentlyof all other responses. There are several important points tobe noted in the use of these graphs:1. In the case of multiple feedback networks such as in Figure

6, the response with the lowest noise gain at any givenfrequency will be the dominant feedback path. In Figure6 this dominant feedback path is labelled A .

2. Whenever the noise gain and open loop gain intersectwith a combined slope, or rate of closure, exceeding 20dB/decade, poor stability will result. 40 dB/decade willdenitely oscillate since this represents 180 degrees ofphase shift. An example of this is shown in Figure 5.

+VS

VS

R1

IO = I IN

I IN

R2

IO

(MUST BETRUE

CURRENTSOURCE)

R1R2

FIGURE 9. CURRENT MIRROR

Z F

Z I

+V S

V S

V O

V FB

V IN

=V FB

V O=

Z IZ FZ I +

FIGURE 10. FEEDBACK FACTOR,

0.1

+VS

VS

R S

IO

RF

IO = -10A/Volt input

R I

R IV IN

R F

10K

10K

10K

10.0007K

PA07

R C

C C

*

*

Zo =43K withEXACT R , RVALUESSHOWN

F I

OPTIONAL COMPENSATIONSEE TEXT*FIGURE 8. ACTUAL PA07 VCCS

R I + R F2foR IRS

Ceq =


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Apex Voltage to Current Conversion