OPERATIONAL AMPLIFIERS -- GAIN & OFFSET
In looking at sensors we often find that the voltage produced is both low and (with the exception of the bridge) has a large offset. As an example the temperature sensor, LM335, is zero at absolute zero, -273C. With an output of 10 mv/K the signal at room temperature (300K) is 3 volts. This is a nice signal but requires a sensitivity of 5 mv to indicate temperatures of 1/2C. With an AD590 having a sensitivity of 1mv/C (using a 1 Kohm resistor) at 300K the voltage produced is 0.3 volts. To achieve resolution of 1/2C with this transducer the voltages must be measured to 0.5 mv.
This is possible when using a 4 3/4 digit DMM. However when using a 5 volt analog-to-digital converter to achieve 5 mv resolution would require a 10 bit A/D converter. The AD0817 which you purchased for this course has 8 bits. That means that any signal can be broken into 2 to the 8th power, 256 bits. 1/256 is about 0.4% which is sufficient sensitivity for many investigations, even if the dynamic range is rather limiting. However with the AD0817 with a 5.12 volt range, the resolution is 20 mv! With an AD590 (or even worse the thermocouple with a sensitivity of 50 microvolts/C) it is clear that something needs to be done.
The above dilemma can be solved with Op-Amps! We will do several things with OpAmps that will help the problem. Amplification (gain setting) and offset (zero setting) will be considered but other things like filtering out the noise will be left to the student to investigate in the reading assignments. Tompkins is particularly good on Op-Amps, pages 1-18. Specifically pages 1-9 are worth carefully studying.
Thompkins gives two rules useful to understand the workings of an ideal amplifier in the circuit. Learn the principles and you will have an easy time of understanding the circuits involving op-amps.
"Rule 1. When the op amp is in the linear range the two inputs are at the same voltage." (Thompkins page 2)
"Rule 2. No current flows into either terminal of the op amp." (Tompkins page 3)
The first consideration in op-amps to be mastered is the gain, Vo/Vi. Using Tompkins rules and Kirchoff's circuit laws we can establish the gain formulae. Tompkins equations 1.3 and 1.4 are simple to calculate but they are also simple to memorize. If you remember that gain is Rf/Ri for inverting and 1 more for the non-inverting, or 1+(Rf/Ri), this form is easy to remember. The gain and configuration of inverting and non-inverting OpAmps is figure5.gif on the browser.
This was an exercise in determining the gain, saturation and impedance of non-inverting and inverting amplifiers. This is something that is often missed by the novice. Learn these lessons well or you may have to learn them the hard way later; by agonizing over a complex circuit that is acting funny and you don't know why.
A general analog conditioning circuit that will be used a great deal in class. Temperature sensors, as one example, are zero at absolute zero. It would be more convenient if it were zero at room temperature. The sensitivity of temperature of less than one degree is adequate for most engineering work but we will find that A/D converters will limit the resolution unless signal conditioning is used. The circuit on page 62 will be very useful to matching transducers to A/D converters. In addition it provides an initial buffering amplifier that will prevent sensors from being loaded.
If you look at the general form of a signal conditioning circuit from the Lab Topics hot key or pressing on the highlighted words in this paragraph you will see a blank form to configure your circuit as well as a summary of how to wire both inverting and non-inverting amplifiers.
Now how would you develop a circuit to use with an AD590 sensor over a range of 100 degrees C. This sensor has a sensitivity of 1 mv/C (when using a 1 Kohm current measuring resistance)? Thus the range would be 100 millivolts, 0.1 volts. The gain output volts of a typical A/D converter, AD0817, is 5 volts. The output, 5 volts, divided by the input, 0.1 volt, is 50; the gain required. (You might consider the differences between this OpAmp method and the circuit in the discussion of Wheatstone bridges)
For a range from -40 C to 60 C, absolute temperature is 233 K to 333 K. The voltage a -40 C would be zero and at 60 C would be 5 volts. The voltage offset would be the offset would be -0.233 volts (1mv/degree K, before the gain of 50 is applied). This low a voltage may pose a problem, since it is difficult to set the 15 turn pot using a -15 supply voltage.
A voltage reference chip that should be quite useful is the LM336 which gives an output of 2.5 volts. Locate the LM336-2.5v Specification Sheet used in previous laboratories. Set up an OpAmp as an inverter with a gain of 1.0. Drive the 15 turn pot with a -2.5 volt source from the output of the inverting opamp.
Since the current drain in an inverting amplifier is dependent upon Ri, the value you select should be large, say 100K. Set a 15 turn pot to the required -0.233 volts. (When we need a more stable voltage reference for the A/D (AD0808 or AD0817) we will then want to use the temperature correction circuit; For now use the less complex circuit.) With these considerations you can draw a circuit with specific resistance values for both the LM335 and the AD590. Each will be different since they have different sensitivities. Review the comments and spec sheets from the temperature laboratory exercise, Lab 2.
The A/D converter that we will be using, AD0808 or AD0817, is limited to 0 to +5 volts on the input. Thus we need to find a way to insure that this is accomplished. A Zener diode with a 5.1 volt breakdown voltage will be installed across the final amplifier; The gain amplifier. This will limit the voltage between 0 and 5.1 volts --approximately. Always include this zener diode in any circuit using the A/D converter we use in class. There are bipolar A/D that can accept voltages from -10 to +10, IC 7109. Then the zener diode is not needed. You may also use a separate amplifier that uses +5 volts and ground which will limit the voltages to these rails. This will require a separate amplifier chip.
BRING TO LABORATORY 3 CIRCUIT DIAGRAMS (use Figure 5 print out) WITH RESISTANCE VALUES SELECTED AND REFERENCE VOLTAGE CIRCUITS SPECIFIED: