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Whenever a DC voltage is converted into digital format, there is always some loss of resolution due to the incremental nature of the conversion. For instance, an 8-bit converter will divide the input voltage range into 256 increments, or voltage steps. If the input voltage range is 0 to 10.0 volts, this will yield increments of about 39.1 mv. A 12-bit converter will improve this resolution considerably by dividing the input scale into 4096 increments. For the same 0 to 10.0 volt input, the increment would be 2.44 mv. It is easy to see that increasing the "bit resolution" of the analog converters will increase the resolution.

This application note describes some "tricks" that are very easy to implement and can increase the effective bit resolution of your input voltage scale. For many DC voltage measurements, you do not need the complete voltage range that the FT-100 provides. If the voltage range of interest is scaled to the full FT-100 input voltage range, the resolution of the reading will increase. Suppose, for instance, that your circuit has a reference voltage that must be set to 1.20 +/-0.01 volts. Using the 0-10 volt input on the FT-100 only allows you to reach the target within +/-39.1 mv. By scaling an input range of 0.5-1.5 volts to 0-10.0 volts, we have effectively decreased the incremental steps to 3.91 mv. - using only an 8-bit analog converter!

Also, suppose you want to measure a voltage that is outside the range of the FT-100 (or Expansion Modules). The circuits shown here will allow you to scale almost any voltage range. After scaling, the test program will need to compensate for the scaled readings. The compensation formulas are given here as well. Using these circuits allow you to take full advantage of the analog input measurement capabilities of the FT-100.

The circuits shown here are very universal and should cover most voltage scaling applications. In general, the operational amplifiers shown may be any universal op-amp. Depending on the accuracy desired, you might need to consider the individual op-amp characteristics, especially such things as the input offset voltage, input voltage range, etc.. Because all components have tolerances, trimmer potentiometers would be recommended for the gain feedback resistor (R2 in figure 1). Depending on the overall accuracy desired, the bias voltage may need to be derived from a precision voltage source.

There are a few things that should be considered when designing the scaler circuit:

- The input impedance is determined almost solely by R1. Try to make R1 as large as practical.
   Values up to 100KW should work fine. If a higher input impedance is desired, use another
   op-amp as a voltage follower.

- The bias voltage (V_BIAS) must be within the working voltage limits of the op-amp input.
   (V_BIAS between -10.5 and +10.5 volts should work fine).

- The bias voltage must be derived from a voltage source as stable and accurate as your
   measurements dictate. The voltage reading will be only as accurate as your bias voltage.

- Resistors should be low tolerance, high quality - 1% metal film.

- By-pass capacitors should be used liberally.

- Ground lines should be hefty and as short as possible.

FIGURE 1 - DC Voltage Scaler

The first step to designing your scaling circuit is to determine the overall voltage gain (A_V). The voltage gain is defined as:

(EQUATION 1)

A_V = ABS (Output Voltage Range / Input Voltage Range) =  ABS ((V_OH - V_OL) / (V_IH - V_IL))

Where: A_V = DC voltage gain.
V_IH = High end of input voltage range.
V_IL = Low end of input voltage range.
V_OH = High end of output voltage range (FT-100 input).
V_OL = Low end of output voltage range (FT-100 input).

The DC voltage gain is determined by the resistors R1 and R2 in the following formula:

(EQUATION 2)

A_V = R2 / R1    or     R2 = A_V / R1

We must select R1 and R2 to yield the desired gain. The exact values are not overly critical as long as the op-amp is not overstressed. In general, keeping R1 and R2 above 1K should always be safe. Remember, R1 sets the input impedance.

In order to offset the output voltage range, we must now determine the bias voltage (V_BIAS) by using the following formula:

(EQUATION 3)

V_BIAS = ((A_V * V_IH) - V_OL) / (A_V + 1)

The bias voltage is determined by the voltage divider consisting of resistors R3, R4, and R5. Normally the bias voltage should be somewhat adjustable to allow for routine calibration.

Using these formulas, you should be able to scale your input voltage to the full scale input of the FT-100. Since the actual voltage being read by the FT-100 is a scaled voltage, and not the actual voltage input, you will need to scale the voltage reading in your program using the following formula:

(EQUATION 4)

V = V_BIAS - ((V_IN - V_BIAS) / A_V)

It may be best to look at some examples to get a better idea of how all these formulas work.

EXAMPLE #1

Given: Voltage range to be read = -2.0 to +2.0 volts
          Want to use the FT-100 main unit analog input with a range of 0 to 10.0 volts

Using Equation 1, we find that our DC voltage gain is:

A_V = ABS ((10.0 - 0.0) / (2.0 - (-2.0))) = 2.5

Where: V_IH = 2.0             V_OH = 10.0
            V_IL = -2.0             V_OL = 0.0

We can now use Equation 2 to select R1 and R2 for a gain of 2.5. We will arbitrarily select R1 to be 100KW. This yields the following:

R2 = (2.5 * 100000) = 250000 = 250 K ohm

The bias voltage may be determined now, using Equation 3:

V_BIAS = ((2.5 * 2.0) + 0.0) / (2.5 + 1) = 1.43 volts

Now that we know all the critical elements, we can now build the circuit and fine tune any voltages as needed. The final circuit would look like:

FIGURE 2 - EXAMPLE #1 FINAL SCHEMATIC

In order to read the correct voltages, the FT-100 must "correct" the scaled input voltage. Using Equation 4, the command would look like:

V = 1.43-((AA9-1.43)/2.5) (Assuming AA9 is used as the analog input line)

The variable V will now equal the exact voltage present at the input to your scaler circuit.

EXAMPLE #2

Given: Voltage range to be read: -30.0 to +20.0 volts.
          Want to use an Expansion Module with input range of -5.0 to +5.0 volts.

From Equation 1 we get the DC gain:

A_V = ABS ((5.0 - (-5.0)) / (20.0 - (-30.0))) = 0.2

From Equation 2 we once again choose R1 to be 100KW. Solving for R2, we get:

R2 = (0.2 * 100000) = 20000 = 20 K ohm

From Equation 3, we get the bias voltage:

V_BIAS = ((0.2 * 20.0) + (-5.0)) / (0.2 + 1) = -0.833 volts

The compensation formula that must be used in the program to "correct" the analog reading is:

V = -0.833-((AB5+0.833)/0.2) (Assuming AB5 is used as the analog input line)

Figure 3 shows the final circuit with all the selected values.

FIGURE 3 - EXAMPLE #2 FINAL SCHEMATIC

If you have several different voltage ranges that need to be monitored, or if you need high resolution over a larger input range, the circuit shown in figure 4 provides a very economical solution. By using an inexpensive analog multiplexer, such as the DG509, it is possible to have several voltage ranges using the same scaler circuit. The gain feedback resistor and the bias voltage are "switched" as desired. Two digital output lines from the FT-100 are used to automatically switch the multiplexer for the desired voltage range. This can be done within the test program, making it completely transparent to the operator.

FIGURE 4 - MULTIPLE VOLTAGE RANGES AND GAINS

To extend the input range, and maintain a high resolution reading, divide the input range into several sub-ranges. For example, using the circuit shown in figure 4, we can select scaler values for an input range of 0-0.5 volts. Using the previous equations, this can be scaled to 0-10.0 volts output with a resolution of about 1.95 mv. To read a voltage above 0.5 volts, at the same resolution, we can keep the same amplifier gain but change the bias voltage to shift the output (using equation 3). The four input voltage ranges would be: 0-0.5, 0.5-1.0, 1.0-1.5, 1.5-2.0. We are now able to measure voltages from 0.0 to 2.0 volts at a resolution of 1.95 mv. The test program would need to read the input voltage at the lowest scale and determine if the reading is at the top end. If so, simply switch the DG509 analog multiplexer to the next higher voltage range. Continue this until the reading is within the input range.

The DG509 analog multiplexer allows up to 4 different voltage ranges and 4 different gains, but a DG507 increases this number to 8. If the gain can remain constant, as in our previous example, a DG506 will allow up to 16 different voltage ranges! These are all very inexpensive integrated circuits, and are readily available from several sources.

Using these methods, it is very easy to monitor almost any voltage range - and very inexpensively! If you have particular needs and aren't sure how to go about designing your scaler circuit, or if you aren't sure where to purchase or how to use analog multiplexers, give Y-tek a call. An Applications Engineer will be glad to help you.

NOTICE:  Every effort has been made to insure the accuracy of the information contained in this document, however
                  Y-tek is not responsible for any consequences resulting from erroneous or inaccurate information.

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FT-100a Functional Tester

Custom-Designed Test Systems

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