Analog Devices AN-279 Application Notes

AN-279
a
APPLICATION NOTE
One Technology Way • P.O. Box 9106 • Norwood, MA 02062-9106 • 781/329-4700 • World Wide Web Site: http://www.analog.com
Using the AD650 Voltage-to-Frequency Converter As a
Frequency-to-Voltage Converter
By Steve Martin
The AD650 is a versatile monolithic voltage-to­frequency converter (VFC) that utilizes a charge­balanced architecture to obtain high performance in many applications. Like other charge-balanced VFCs, the AD650 can be used in a reverse mode as a frequency-to-voltage (F/V) converter. This application note discusses the F/V architecture and operation, component selection, a design example, and the fundamental trade-off between output ripple and circuit response time.
F/V CIRCUIT ARCHITECTURE
Figure 1 shows the major components of the frequency­to-voltage (F/V) converter. It includes a comparator, a one-shot with a switch, a constant current source, and a lossy integrator. When the input signal crosses the
C
INT
R
INT
V
OUT
COMP
f
IN
–0.6V
C
OS
ONE
SHOT
Figure 1. Circuit Architecture
threshold at the comparator input, the comparator triggers the one-shot. The one-shot controls a single pole double throw switch which directs the current source to either the summing junction, or the output, of the lossy integrator. When the one-shot is in its “on” state, there is current injected into the input of the integrator and its output rises. When the one-shot period has passed, the current is steered to the output of the integrator. Since the output is a low impedance node, the current has no effect on the circuit and is effectively turned off. During this time the output falls due to the discharge of C
through R
INT
. When constant
INT
triggering is applied to the comparator, the integration capacitor will charge to a relatively steady value and be
REV. B
maintained by constant charging and discharging. The charge stored on C
is unaffected by loading
INT
because of the low output impedance of the op amp.
THEORY OF OPERATION
Figure 2 shows a simplified representation of the AD650 in the F/V mode. Figure 3 represents the current i(t) delivered to the lossy integrator. The current can be thought of as a series of charge packets delivered at
1
f
=
OS
IN
with constant amplitude (α) and
T
)
C
INT
R
INT
V
OUT
i(t)
frequency
duration (t
Figure 2. Simplified Schematic
i(t)
t
OS
T
t
Figure 3. Current i(t) into Integrator
From inspection of Figure 3, the average value of input current is found by dividing the area of the current i(t) by the period T. The dc component of the output voltage is found by scaling the average input current by the feedback resistor R
V
OUTAVG
=×α.
.
INT
t
OS
R
T
INT
(1a)
Equation 1a becomes a linear function of frequency
when f
is substituted for
IN
VtRf
OUTAVG OS INT IN
=× ××α
1
.
T
(1b)
AN-279
Notice that the relationship between the average output voltage and input frequency is a function of the one-shot time constant and the feedback resistor but not of the integration capacitor. This is because the integration capacitor is an open circuit to dc. From Equation 1b it is clear that the most practical way to trim the full-scale voltage is to include a trim potentiometer in series with R
. Typically, a 30% trim range will be required to
INT
absorb errors associated with t
and α.
OS
It is also important to characterize the transient response of the integrator in order to determine settling time of the F/V to a step change of input frequency. The transfer function of the lossy integrator is given in the frequency domain by:
1
VS
()
OUT
IS
()
IN
=
C
INT
S
+
RC
INT INT
1
(2)
×
which indicates that the natural or step response to a change of input frequency is governed by an exponential function with time constant π = R
INT
× C
INT.
With the average output voltage and transient response known, the peak-peak output ripple can be determined using Equation 3. Once this is determined, a design algorithm can be developed (Reference 1).
The peak-peak ripple is given by:
//
tRC
()−()
OS OS
eee
V
=
PP
TIRC
−+
1
e
TIRC
Tt RC
1
××
α
R
(3)
where:
t
= one-shot time constant [seconds]
OS
T
= period of input frequency (1/fIN) [hertz]
R
= integration resistor [ohms]
C
= integration capacitor [farads]
α = current source value (1 mA for AD650) [amps]
Equation 3 accurately represents the ripple amplitude for a given design. The following section shows how this equation is used as an iterative part of the total solution. Equation 3 can also be used to illustrate how the ripple amplitude changes as a function of input frequency. It is interesting to note that the ripple amplitude changes only moderately with input frequency and has its largest magnitude at the minimum frequency.
DESIGN PROCEDURE
Recall from looking at Figure 3, that the one-shot “on” time will be some fraction of the total input period. This is the time that the circuit integrates the current signal α. The output ripple can be minimized by allowing the current source to be on during the majority of this period. This is achieved by choosing the one-shot time constant so that it occupies almost the full period of the input signal when this period is at its minimum (or the input frequency at its maximum). To design safely and allow for component tolerance at f
, make t
MAX
OS
approximately equal to 90% of the minimum period. Given t C
OS
, the value of the one-shot timing capacitor,
OS
, is determined from Equation 1 in the AD650 data sheet. This equation has been rearranged and appears here as:
t sec
−×
C
where
(NOTE: For maximum linearity performance use a low dielectric absorp­tion capacitor for COS.)
OS
=
OS
t
OS
×
6.8 10
is in seconds and
7
3
10
3
sec F
/
C
is in farads.
OS
(4)
Once COS is known, the integration resistor is uniquely determined from the full-scale equation (Equation 1b), since t
, α, fIN, and V
OS
are known. This leaves only the
OUT
integration capacitor as the final unknown.
C
is chosen by first determining the response time of
INT
the device being measured. If, for example the frequency signal to be measured is derived from a mechanical device such as an aircraft turbine shaft, the momentum of the shaft and the blades should be used to determine the response time. The time constant of the F/V is then set to match the time constant of the mechanical system. It may be set somewhat lower, depending on the desired total response time of the mechanical and electrical system. Remember to allow several time constants (N) for the F/V to approach its final value. For the first iteration of C
use the following
INT
expression:
C
Mechanical sponse Time
=
INT
Re
×
NR
INT
(5)
where N is the number of time constants chosen to allow adequate settling. Table I may be used to determine the number of time constants required for given settling accuracy.
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REV. B
AN-279
DETERMINE VARIABLES: f
MIN
, f
MAX
RESPONSE TIME , FULL-SCALE VOLTAGE, MAXIMUM ACCEPTABLE RIPPLE.
CALCULATE: tOS = 0.9/f
MAX
FIND COS GIVEN t
OS
USING
EQUATION 4.
FIND R
INT
GIVEN V FULL-SCALE
AND t
OS
USING EQUATION 1b.
DETERMINE N BY SYSTEM ACCURACY
USING TABLE I (DEFAULT TO 6 IF UNSURE).
FIND C
INT
USING EQUATION 5.
DECREASE N TO
TRADE RESPONSE
TIME
FOR RIPPLE
CALCULATE RIPPLE USING EQUATION 3
AND f
MIN
.
RIPPLE
TOO
LARGE?
C
INT
IS KNOWN.
DESIGN
COMPLETE.
YES
NO
Table I. Settling Accuracy vs. Number of Time Constants
# of Time Constants (N) # of Bits % Accuracy
4.16 6 1.6
4.85 7 0.8
5.55 8 0.4
6.23 9 0.2
6.93 10 0.1
7.62 11 0.05
8.30 12 0.024
9.00 13 0.012
9.70 14 0.006
10.4 15 0.003
11.0 16 0.0015
A larger number of time constants will give a more responsive circuit but will also increase the ripple at the F/V output. A practical approach is to start with 8-bit settling accuracy, using N = 6 time constants, and increase or decrease N depending on ripple content.
The ripple content is calculated using Equation 3. Remember that the ripple amplitude will change with frequency and will be largest at the lowest frequency. It is also important to note that while in some cases the ripple amplitude may be large, the average value of the output voltage will always represent the input frequency (unless the ripple gets too close and “clips” at the positive supply rail). Figure 4 shows an example of how output ripple amplitude will change with input frequency for a typical application. This graph was obtained by plotting Equation 3 over the full range of input frequencies. For design purposes it is only necessary to calculate ripple at the worst case frequency (f
). Figure 5 summarizes the design procedure.
MIN
DESIGN EXAMPLE
The rpm of an automobile’s engine is to be monitored for use by an on-board computer. The rpm signal that will be generated from an F/V converter is to be digitized with an 8-bit A/D converter. The rpm range of the engine extends from 300 rpm to 7000 rpm. A 200-tooth flywheel at these rotational speeds will generate pulses from 1 kHz up to 23 kHz. The response time to a step change in throttle position of the engine has been measured, in neutral, to be 400 ms. The goal is to design an F/V converter that will respond at approximately the same rate as the engine, or faster, and will have ripple that is undetectable by the A/D converter. The A/D converter has a 10-volt full scale.
1. Let t
be 0.9 × 1/f
OS
= 0.9 × 43.5 µs = 39 µs.
MAX
2. Find COS = 0.0057 µF (from Equation 4) (an impractical value for polystyrene, but tantalum may be used with reduced linearity).
V
3.
R
=
INT
mA s kHz
13923
10
××
=
11.14µΩ
k
(from
Equation 1b).
0.015
0.011
– p-p
0.008
OUT
V
0.004
0.000 1000 6500
Figure 4. P-P Ripple vs. Frequency (See Design Example)
REV. B
RIPPLE VS. FREQUENCY
12000 17500 23000
f
IN
Figure 5. Design Flowchart
–3–
AN-279
(If R
, the load seen by the amplifier, is less than
INT
1kΩ, then t
4. From Table I, an RC network can settle to eight bits in six time constants so:
C
=
INT
5. Ripple = 6.25 mV @ 300 rpm and 0.67 mV @ 7000 rpm (from Equation 3).
6. 1/2 LSB size for an 8-bit converter with 10 V full scale is 19.5 mV. Fortunately, the ripple is below the quantization level on the first iteration. If desired, the integration capacitor may be lowered to reduce response time of the F/V converter.
7. Guessing C program gives a maximum ripple content of 12.5 mV and a response time of 200 ms.
THE TRADE-OFF BETWEEN RIPPLE AND RESPONSE TIME
In many instances some compromise must be made between ripple and response time. If response time is of primary importance, the integration capacitor may be lowered at the expense of increased ripple. Similarly, if ripple is paramount, the integration capacitor must be increased resulting in slower response. The design procedure outlined above assumes that ripple content is the less desirable effect. Rather than increasing C low-pass filter could be used, but this also slows the response time. An approximation to determine total response time of two cascaded systems, each with separate response times, can be found by using the “root sum of squares” technique.
TTT
TOTAL A B
This leads to the “three-to-one” rule, i.e., if TA is more than three times T be ignored, hence, T system.
must be reevaluated.)
OS
ms
40610
1146.
(
)
INT
=+
=
F
µ
.
k
= 3.0 µF or using an iterative computer
22
and their squares are added, TB may
B
is the total response time of the
A
INT
, a
SUMMARY
Low cost voltage-to-frequency converters can be used in the frequency-to-voltage mode. Trade-offs exist between output settling time and ripple with the selection being application-specific. However, by using the design guidelines highlighted in this note, optimized performance can be achieved in many applications.
References
1
McGillem, C. D., and G. R. Cooper,
Discrete Signal and System Analysis
Continuous and
, Second Edition.
New York: CBS College Publishing, 1984.
2
Analog Devices Inc. AD650 Data Sheet. Latest version
can be found on www.analog.com.
15.5mV
200␮s
100
0%
V1
90
10
5mV
Figure 6. Typical Ripple Output
100.10ms
t1.70V
20ms
100
0%
A1
90
10
1V
Figure 7. Response to Step Change in Frequency
E01373–0–9/00 (rev. B)
–4–
PRINTED IN U.S.A.
REV. B
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