Fundamentals Of Analog Electronics 291t15

fu. Calculating Zf or using the LabVIEW vector calculator shows in the limit of low frequencies high frequencies

(f< fu), Zf -> Rf

(5-16)

(f> fu), Zf -> 1/j2πfCf

(5-17)

At low frequencies, the reactance of the capacitor is so large, that all the current flows through Rf and the gain is just (Rf/R1). At high frequencies, the capacitor reactance is low and the current readily flows through the capacitor not the resistor. Now the gain is (1/j2πf R1Cf) and falls off inversely with frequency. On the Bode plot, this region is a straight line with a negative slope of 20 dB/decade. When a square wave is integrated, what waveform do you find? That is right, a triangular wave. Just like in Lab 2 for the DC integrator, the capacitor Cf allows charge to accumulate on the capacitor in the region where f> fu. A low filter in this frequency range integrates the waveform so that a square wave input becomes a triangular wave output. AC integrators find extensive use in analog computation circuits.

High Filter A simple high filter can be formed by adding a capacitor C1 in series with the input resistor R1 of an inverting op-amp circuit.

© National Instruments Corporation

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Fundamentals of Analog Electronics

Lab 5 Op-Amp Filters

Rf R1

C1

+15V -

A Vin

+ -15V

Vout

Figure 5-3. High Op-Amp Circuit

Recall that “resistors” in series add serially. The input network of components can be represented by a single impedance Z1 where Z1 = R1 +Xc

(5-18)

Substituting the definition of reactance for a capacitor leads to Z1 =(R1- 1/jω C1)

(5-19)

The complex transfer equation for gain can be written as Vout = (Rf / Z1) Vin

(5-20)

Solving for the gain (Vout / Vin) leads to G(f) = G(0)/√(1+fl2/f2)

(5-21)

where G(0) = Rf /R1. This is similar in form to the previous Equation 5-13 except that the frequency ratio is inverted. Here fl is a low frequency cutoff point and is governed by the input components R1,C1 and the equation 2πfl = 1/ R1C1

(5-22)

In this configuration, the op-amp circuit is AC coupled and no DC signal can . Only AC signals with a frequency greater than the low frequency cutoff point will be amplified fully. Note at f = fl, the gain has fallen to 1/2 or –3 dB. The filter bandwidth is now (fu - fl) where fu is the closed loop gain upper cutoff frequency.


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Lab 5

Op-Amp Filters

LabVIEW Demo 5.2: Simple High Filter Load the program called High.vi from the chapter 5 program library. Click on the Run button to see the Bode plot. Investigate the position of the low frequency cutoff point as the input capacitor or resistor is varied. Note also the response curve when the gain G(0) is changed by varying R1or Rf. For convenience the open loop curve with A(0) = 100 dB and an open loop cutoff frequency at 10 Hertz is also shown.

Figure 5-4. Bode Plot of an Op-Amp High Filter

All frequencies greater than fl have a constant gain (up to the open loop cutoff) while all frequencies less than fl are attenuated. A filter which displays this property is called a high filter. For low frequencies, the response curve rolls off with a slope of 20 dB/decade. What is happening here? Look at the input network impedance in the limits where f< fl and f>fl. Calculating Z1 or using the LabVIEW vector calculator show that in the limit of low frequencies (f< fl), Z1 -> 1/j2πfC1 high frequencies

(f> fl), Z1 -> R1

(5-23) (5-24)

At low frequencies, the reactance of the capacitor is so large that current is strongly attenuated and the gain (j2πf RfCf) increases linearly with frequency up to fl. On the Bode plot, this region is a straight line with a positive slope of 20 dB/decade. At high frequencies, the capacitor reactance is low and the current readily flows through the input capacitor. The gain acts as if there were no capacitor in the input loop and the gain is constant (Rf /R1) up to the open loop frequency response curve.


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What happens when a triangular waveform is applied to a high filter in the region where the gain is frequency dependent? That’s right, the output is a square wave. The harmonic components of the triangular wave are strongly modified so that the input signal is differentiated. AC differentiators find extensive use in analog computation circuits and noise suppression circuits.

Band Filter A band filter es all frequencies between two cutoff points at a low and a high frequency. An ideal band filter would be infinity sharp at the cutoff points and flat between the two points. Real band filters with names like Chebyshev, Butterworth and Elliptic come close to the ideal but never quite make it. A simple band filter can be made by combining the simple high and low circuit of the previous sections.

Cf

R1

C1

Rf +15V

-

A Vin

+ -15V

Vout

Figure 5-5. Schematic Diagram of a Op-Amp Band Filter

Both the input and loop impedances are now complex and the gain is G(f) = |Zf /Z1|

(5-25)

Solving this gives the frequency dependent gain G(f) = G(0) /[√(1+fl2/f2)][ √(1+f2/fu2)]

(5-26)

with a low frequency cutoff point fl (Equation 5-22) and a high frequency cutoff point fu (Equation 5-15). The bandwidth of the band filter is given from the intersection points of the –3 dB line with G(f) or simply BW = (fu-fl).


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Lab 5

Op-Amp Filters

LabVIEW Demo 5.3: Simple Band Filter Load the program called Band.vi from the chapter 5 program library. Click on the Run button to see the Bode plot. Investigate the shape of the band filter curve when the key components R1, C1, Rf or Cf are varied. For convenience the open loop curve with A(0) = 100 dB and an open loop cutoff frequency at 10 Hertz is also shown.

Figure 5-6. Bode Plot of an Op-Amp Band Filter

What shape does the band filter response curve take when fu = fl? Such a curve selects one frequency above all the others.

LabVIEW Challenge What happens when a square wave is used as the source waveform Vin for a low filter? A square wave is made up of a fundamental sine wave at frequency f and higher odd harmonics at 3f, 5f ,7f etc. The amplitudes of each frequency component are 1, 1/3, 1/5, 1/7 etc. When a square wave is applied to the filter in the region where the gain is frequency dependent, the harmonics are rapidly attenuated, so much so that the output voltage is modified or filtered into a triangular waveform.


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Design a LabVIEW program which adds the fundamental and three harmonics of a square wave and is displays the resultant waveform for one complete cycle. Apply this waveform to an op-amp with a gain of 1000 and an upper cutoff frequency at the waveform fundamental frequency. What is the amplitude for each component? Add these components to see an approximation of a triangular wave

eLab Project 5 Objective To study the frequency response of a band filter and its dependence on a series capacitor in the input loop and a parallel capacitor across the resistor.

Procedure Build a real band filter using the circuit shown below. With a function generator as a source of sine waves measure the frequency characteristics and determine the Bode plot. 0.001 µfd

100 kΩ

10 kΩ

1.0 µfd

+15V 2 3

Vin

7

741 +

4

6

-15V

Vout

Figure 5-7. Schematic Diagram of a Band Filter

The circuit requires a 741 op-amp, two resistors, two capacitors and two power supplies. Choosing Rf = 100 kΩ and R1 = 10 kΩ gives the closed loop gain of 10 or 20 dB in the band frequency region. Chose C1 = 1µf and Cf = 0.001µf. Chose a function generator set to sine wave with an


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Lab 5

Op-Amp Filters

amplitude of 50 mV as the input voltage Vin. Component layout is shown below.

Figure 5-8. Component Layout of an Op-Amp Band Filter

Use an oscilloscope or a high speed DAQ card to measure the output signal level. In all cases, it is wise to measure the input signal level and compute the gain from the expression Vout/Vin. In choosing the test frequencies, select the decade range then measure at multiples of 1, 2, 4, and 8. This gives an approximately uniform set of points on a log f scale. Graph the Bode plot, that is the gain in decibels as a function of log10 of the frequency. From the key variables R1, C1, Rf or Cf calculate the lower and upper frequency cutoff points. How do these points compare with the actual measured –3dB points on the Bode plot?

Computer Automation 5: Response to Stimulus Signals Computer automation is all about the automated measurement, analysis and reporting of the response of devices or systems under test. For AC stimulus, the response of interest could be the amplitude, the frequency or the phase content. In all cases, a representative sample of the signal in the form of an array is the most convenient to analyse. LabVIEW has many array VIs that enable the amplitude to be measured in units of peak, peak-peak, average or rms signal level. The frequency of sinusodial signals can be measured eloquently with frequency, period or counter VIs. The harmonic content of more complex stimulus signals can be analysed with FFT or Power © National Instruments Corporation

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Spectrum VIs. Phase measurements require a reference signal and it is best to store the reference and response signals as an array. In this lab, we look on at sinusodial stimulus signals applied to a band filter and observe the response on a LabVIEW graph. Launch the LabVIEW program entitled Response 5.vi from the chapter 5 library. This program uses an input channel on the DAQ card to measure the circuit response signals. Connect a waveform generator sinusodial output (1volt peak signal level) to the input (pin 3) of the band filter, eLab 4. Choose components so that the low frequency cutoff is about 50 Hertz. Click on Run to start the data collection and observe the waveform as the stimulus is varied from 1 to 100 Hertz. Adjust the stimulus frequency until the measured response is –3dB below the input level. This frequency is the low frequency cutoff point. How does it compare with the value predicted from Equation 5-21?

LabVIEW Enhancements Design a LabVIEW VI to determine the peak, peak-peak or rms signal amplitude. Replace the waveform generator with a LabVIEW generator. Design a LabVIEW VI to automatically sweep the input frequency and determine the low frequency cutoff point.


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Lab 6 The 555 Timer Chip Astable Circuit Introduction The 555 IC is unique in that it simply, cheaply, and accurately serves as a free-running astable multivibrator, square-wave generator, or signal source, as well as being useful as a pulse generator and serving as a solution to many special problems. It can be used with any power supply in the range 5-18 volts, thus it is useful in many analog circuits. When connected to a 5-volt supply, the circuit is directly compatible with TTL or CMOS digital devices. The 555 timer can be used as a monostable multivibrator (one-shot), as an astable multivibrator (oscillator), as a linear voltage ramp generator, as a missing pulse detector, as a pulse width modulator and in many other applications. Clocked digital logic devices are synchronous with an internal clock of some form. Computer and real time clocks use crystal controlled oscillators as the internal standard. Slower devices such as digital multimeters and consumer electronics often use oscillators whose timing is dependent on the charging and discharging of a simple RC network. In this lab, we look at one such device, the 555 timer chip, as a free-running (astable) oscillator.

555 Timer Chip The astable configuration of the 555 circuit, shown below uses two resistors and a capacitor to define the oscillator frequency. The voltage across the external capacitor is measured at the trigger and threshold inputs (pins 2 and 6 respectively). Depending on the magnitude of this voltage, an internal RS flip-flop may be set or reset. This output places the circuit into a charge or discharge cycle. On charging, the capacitor voltage rises to 2/3 Vcc and on discharge the capacitor voltage falls to 1/3 Vcc. At the upper limit, the threshold input turns off the internal flip-flop, and at the lower limit, the trigger input turns it on. The output voltage (pin 3) is a buffered copy of the flip-flop output and hence is a digital signal. The resulting pulse waveform defines the 555 oscillator signal.


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Lab 6 The 555 Timer Chip Astable Circuit

V cc

4 RA

3

555 7

RB

8

6 2

Output

Discharge Threshold 5

Trigger 1

C

Control Voltage

C = 0.1 µf

(optional)

Figure 6-1. The Basic 555 Astable Circuit

The frequency of oscillation depends only on the resistor-capacitor chain (RA,RB,C) and is independent of the power supply voltage Vcc. On charging, the external capacitor C charges through resistors RA and RB. The charging time t1 is given by t1 = 0.693 (RA + RB) C

(6-1)

and this part of the cycle is signaled by a high level on the output (pin3). On discharge, the external capacitor C discharges through the resistor RB into pin 7 which is now connected internally to ground. The discharge time is given by t2 = 0.695 RB C

(6-2)

and this part of the cycle is signaled by a low level on the output. The total time for one oscillation (the period T) is given by the sum of these two times T = t1 + t2 = 0.695(RA + 2RB) C

(6-3)

The frequency F is given by the reciprocal of the period, or F = 1.44/(RA + 2RB)C

(6-4)

With the appropriate choices of external timing components, the period of the oscillation can range from microseconds to hours. Fundamentals of Analog Electronics

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Lab 6

The 555 Timer Chip Astable Circuit

The duty cycle DC is the ratio of the time the output is low as compared to the period DC = RB/(RA + 2RB)

(6-5)

The duty cycle is always less than 50% or saying it another way, the off time t2 is always less than the on time t1. Thus the output of the 555 astable circuit is asymmetric. By making RB large compared to RA, the waveform becomes more symmetric and the 555 output approaches a square wave.

LabVIEW Demo 6.1: The 555 Astable Oscillator Circuit Load the program called 555Astable1.vi from the chapter 6 program library. Click on the Run button to activate the astable circuit. The output on pin 3 is a digital signal, it is either a high or low level. Investigate how the output waveform changes with different values of RA, RB or C. Observe the output waveform and the duty cycle in the following cases: •

RA > RB,

•

RA < RB,

•

RA = RB.

Figure 6-2. LabVIEW Simulation for a 555 Astable Circuit


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A variable frequency source can be made by selecting capacitors whose values are decades (factors of ten) different from each other and a variable resistor for fine frequency tuning. In practice, RA and RB can have a resistance from 1 kΩ to 10 MΩ and the capacitor can range from 0.001 to 100 µf. These combinations give the 555 astable circuit truly a very wide frequency range.

How Does it Work? The 555 timer is based on the sequential charging and discharging of the external capacitor. Two internal op-amps configured as comparators set the lower and upper voltage limits to 1/3 Vcc and 2/3 Vcc. The voltage across a capacitor at any time t is given by the expression V(t) = V(0) exp(-t/RC)

(6-6)

where V(0) is the initial voltage and RC is a charging/discharge time constant.

LabVIEW Demo 6.2: 555 Astable Oscillator Timing Diagram Load the program called 555Astable2.vi from the chapter 6 program library. Click on the Run button to activate the astable circuit. The timing diagrams for the output voltage (pin 3) and the capacitor voltage (pins 2 & 6) have been added to the front display. While the output (pin 3) is high, the power supply (taken here as +5 volts) charges the capacitor through the resistors RA and RB and the capacitor voltage rises exponentially. When the voltage across the capacitor reaches a reference voltage of 2/3 Vcc (3.33 volts), the threshold comparator (at pin 6) triggers an internal flip-flop which resets the output (pin 3) low and starts the discharge cycle. The voltage at the upper limit is 3.33 = 1.67 exp(-t1/[RA +RB]C)

(6-7)

Solving for t1 in Equation 6-1 yields the time interval that the capacitor is charging. The timing diagram shows the charging cycle (green trace capacitor voltage) as a positive ramp when the astable output (red trace output pin 3) is at the high level. The two comparator limits 1/3 Vcc and 2/3 Vcc are shown as horizontal lines (white traces).


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Lab 6


Figure 6-3. LabVIEW Display of the Charge and Discharge Cycles for a

555 Astable Circuit

When the capacitor voltage reaches the upper reference limit, the power supply is effectively removed from the capacitor circuit and pin 7 becomes internally connected to ground. The capacitor is allowed to discharge through the single resistor RB. The discharge voltage at the lower limit is 1.67 = 3.33 exp(-t2/RBC)

(6-8)

where t2 is the discharge time constant. In the discharge cycle, the capacitor voltage ramps down (green trace) to the lower limit (1/3 Vcc). At this point the trigger comparator (pin 2) sets the flip-flop back to its high state and the cycle repeats.

LED Flasher A flashing alert signal can be generated by driving a light emitting LED diode with a 555 astable circuit. The output (pin 3) is capable of sourcing a few milliamps or sinking up to 200 milliamps, more than enough current to brightly illuminate any light emitting diode.

LabVIEW Demo 5: The 555 LED Flasher Circuit Load the program called 555Flasher.vi from the chapter 6 program library. A LED has been added to pin 3 and pulled up to Vcc through a series resistor. Click on Run to observe the LED flashing. A logic probe has also been added to pin 3. Whenever the output is high, it is red and whenever the output is low, it is black. The LED has the opposite state. Whenever the output is high, it is gray (off) and whenever the output is low, it is yellow (on). The output timing diagram and a frequency counter have also been added to the circuit.


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Figure 6-4. LabVIEW Simulation for a 555 LED Flasher Circuit

When the output (pin 3) is high, there is not enough voltage drop across the resistor and LED to turn the LED on. However when the output is low, current can flow through the LED (which is now forward biased) and into the output (pin 3) and out the ground lead (pin 1). The purpose of the resistor is to limit or to set the current when the LED is on. This resistor determines the brightness of the LED. Since the forward voltage across a silicon diode is 0.6 volts, and if the power supply is 5 volts, then (5 - 0.6) = 4.4 volts will be across the resistor. For a forward bias current of 13.3 ma (red LED brightly lit), the resistor should be about 330Ω.

Temperature Transducer A transducer is an electronic circuit which converts a physical parameter such as temperature into an electrical signal so that it can be measured by conventional techniques. In this virtual experiment, a thermistor is used to convert temperature into a waveform whose off-time is directly proportional to temperature. A thermistor is a device whose resistance is dependent on the device temperature. Thermistors are manufactured from semiconducting materials which s for their unusual conductivity.


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Lab 6


Thermistors have three unique properties; •

The sensitivity or the change in resistance per degree Centigrade is large.

•

The resistance decreases with increasing temperature (a negative temperature coefficient).

•

The resistance has a nonlinear exponential response curve (often over six decades).

LabVIEW Demo 5: Temperature Transducer Load the program called Thermometer.vi from the chapter 6 program library. A thermistor labeled Rb has been placed into a beaker of water. A gas burner controlled by a rotary valve allows you to heat the water to a known themperature. A thermometer has been added to the beaker to measure this temperature and it can be used to calibrate the thermistor. The thermistor replaces the resistor RB in the 555 astable circuit. When run, the waveform will be displayed on an Output vs Time chart. By clicking and dragging the cursors, you can place the cursors on the appropriate transition to measure a time interval ∆t = t2-t1. You can measure the on-time, the off-time or the period. Activate the experiment by clicking on the Run button. Watch the waveform change as the liquid is heated or cooled by changing the gas flow.

Figure 6-5. LabVIEW Simulation to Measure the Heating or Cooling Curve of Water


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To measure the off-time, click and drag the cursor T1 to a falling edge and T2 to the adjacent rising edge such that T2>T1 and read the time from ∆t indicator display. Plot a graph of off-time of the thermistor circuit versus temperature as measured by the thermometer. Is this graph linear or nonlinear? Using Equation 6-2 and other component values (given in the above diagram), calculate the resistance of the thermistor for each temperature measurement.

LabVIEW Exercise Plot a graph of the thermistor resistance versus temperature for this sensor to reveal the unique properties of a thermistor.

eLab Project 6 Objective To study the waveforms from a 555 astable oscillator and its frequency, period and duty cycle dependence on a external chain of resistors and a capacitor.

Procedure Build a LED flasher based on the circuit of Figure 6-1. Connect a 330 Ω resistor and red LED to the output (pin 3). Set RA = 3.3 kΩ, RB = 33 kΩ and C = 0.1 µF. The IC pinout and components can also be seen on the front of the program 555Flasher.vi, Figure 6-4. The component layout is shown below.


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Lab 6


Figure 6-6. Component Layout of a LED Flasher Circuit Using the 555 Timer IC

Measure RA, RB and C separately before adding them into the circuit. Use Equations 6-3 though 6-5 to predict the oscillation period, the frequency and the duty cycle. Measure these same quantities on the output (pin 3) of the 555 IC. How close do the measured parameters agree with the calculated values? Describe the appearance of the LED light. Replace the 0.1 µF capacitor with a 1 µF capacitor and now describe the appearance of the LED light.

Computer Automation 6: Digital Signals For digital signals, the amplitude is a constant and all information is carried in the time response be it frequency, period or duty cycle. In this lab, we will measure the digital frequency produced by a 555 timer chip driven from a +5 volt power supply. Use the eLab project 6 as the starting circuit. As in the eLab 6, choose RA = 3.3 kΩ, RB = 33 kΩ and C = 0.1 µF. Remove the LED from the circuit.


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Launch the LabVIEW program entitled FrequencyLow.vi from the chapter 6 library. This program uses three internal counters on the DAQ card to measure TTL level digital signals in the frequency range f< 1 kHz. Ensure that the counters are connected externally as indicated on the front diagram. Note

That an external 7404 hex inverter chip is also required. Connect the 555 output (pin 3) to the Counter2 input on the DAQ card. Click on Run to make a frequency measurement. that the measured frequency agrees with your frequency prediction based on the component values of RA, RB and C.

Circuit Enhancements Replace the resistor with a variable resistor in the range 10–100 kΩ, and investigate the changes in frequency as the resistor is adjusted. Replace the resistor with a thermistor or a photoresistor and investigate the changes in frequency with temperature or light intensity.

LabVIEW Enhancements For frequencies greater the 1 kHz, a different VI is used. Check your LabVIEW/examples/daq/counter library for a Vi called (Measure Frequency >1kHz.vi). Note that different DAQ cards may use different timers. Ensure you are using the correct library; 8253.llb or AMD9513.llb or DAQ-STC.llb.


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Lab 7 The 555 Timer Chip Monostable Circuit The 555 timer chip introduced in the last lab was configured as a free running astable multivibrator or oscillator. A different circuit allows the 555 timer chip to be configured as a monostable multivibrator or single pulse generator. In this configuration, the IC waits patiently for a trigger pulse which when received causes the output to change state for a fixed period of time related to an external capacitor and resistor, before returning to its initial state. The ability of the monostable to generate a single pulse of precise length is often referred to as a “one shot” circuit element. Many times in digital electronics, a precise delay is required to allow events to be measured, data be displayed for a specific period of time or allow a timing pulse to catch up in order to synchronize events with the clock signal. The 555 monostable is a good solution. One-shots are circuits that generate a fixed-length output pulse after receiving an appropriate trigger signal. The length of the output pulse is generally determined by the charging of a capacitor through an external resistor. A trigger or start signal sets the output on and initiates the charging cycle. When the voltage on the capacitor reaches an upper threshold level of two thirds of the supply voltage, the output is turned off and the capacitor voltage returns immediately to the initial voltage, zero. The circuit is now ready for another trigger pulse.


7-1


Lab 7 The 555 Timer Chip Monostable Circuit

+5V

4

555

100 k Ω 7 1.0 µ F

6 2

+5V Gnd

8 Output

3

Discharge Threshold 5

Trigger 1

(optional) 0.1 µ F

Figure 7-1. The 555 Timer IC Configured as a Monostable Circuit

The monostable arrangement of components requires only a single resistor and capacitor. The voltage across the capacitor is sampled on pins 6 and 7. A negative trigger pulse on pin 2 sends the output (pin 3) high for a time determined by the resistor and capacitor network. When the capacitor voltage reaches the threshold (2/3 Vcc), the output goes low. The on-time Ton is given by Ton = 1.1 R C.

(7-1)

LabVIEW Simulation: Operation of the 555 Monostable Circuit Load the program called Monostable1.vi from the chapter 7 program library. Activate the circuit by clicking on the Run button. Click on the trigger switch to fire the monostable. Investigate the on-time by changing the external resistor and capacitor values.


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Lab 7

The 555 Timer Chip Monostable Circuit

Figure 7-2. LabVIEW Simulation of a 555 Monostable Circuit

In general, the resistor can range from 1KΩ to 3.3MΩ and the capacitor from 500 pf to 10 µF. Thus the on-time can range from microseconds to hours. The trigger input is normally high and momentarily bringing it low generates the trigger signal. It is important to that the trigger input must be brought high again after the triggered low state. For the 555 timer chip, the trigger pulse must be negative and narrower than Ton. Good design calls for a trigger pulse length about 1/4 Ton but shorter times often work well. A graph of Output vs Time Figure 7-3 displays the operation of the monostable more clearly. On triggering, the output pulse (shown in red trace) jumps to the high (positive) state and an internal transistor switch (at pin 7) opens to allow the capacitor to charge. The power supply charges the capacitor through the external resistor. The capacitor voltage (green trace) increases “linearily” from 0 volts to 2/3 Vcc (yellow trace). At this point, the threshold comparator flips state and the internal transistor switch


7-3



is closed forcing the capacitor to discharge and the output to return immediately to zero volts.

Figure 7-3. LabVIEW Display of the 555 Timing Voltages

In the simulation, 5 volts was chosen for the supply voltage so that the output is compatible with standard TTL digital chips. However the chip can be run at any voltage from 5 to 18 volts.

LabVIEW Simulation: Triggered LED Alarm Load the program called Alarm.vi from the chapter 6 program library. A light emitting diode has been added to the output of the 555 monostable circuit. Watch the LED turn on and off, when triggered by clicking on the switch. See the output voltage change and measure the on-time. After activating the circuit with the Run button, click on the trigger switch to generate a single pulse.


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Lab 7


Figure 7-4. LabVIEW Simulation of a 555 Monostable with a LED Output

The LED is pulled high through a 330 Ω resistor whose magnitude was chosen to limit the current flowing through the LED. In the normal state, the output (pin 3) is low and current will through the LED and it will be on. When the output goes high, the LED turns off. A logic probe on pin 3 demonstrates the signal inversion of the LED pulled high.

Photoresistor Sensor The resistance of a few semiconductors is strongly dependent on the amount of light impinging on the material. For these semiconductors, the energy gap is small enough so the photon energy can excite free carriers across the gap. The result is that current flowing through the sensor can be dramatically altered. The resistance of a typical photoresistor can change by six decades (1:1,ooo,ooo) in going from moonlight to sunlight. The resistance in absence of light, the so-called dark resistance is often in the megaohm region. As the light intensity increases, the resistance falls exponentially. In bright light the resistance is small, a few kilo-ohms or less. A plot of the device resistance versus light intensity displays an exponential variation. Plotting the device resistance as a function of the log of the light intensity displays a linear graph. On a logarithmic scale, the light intensity is measured in units of lux. Zero lux is no light while 10 lux corresponds to a bright flashlight beam. Cium selenide, a photoresistance material, has a


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wavelength or colour response close to that of the human eye. The eye is most responsive to the yellow. These devices make good photometers in photography applications.

LabVIEW Simulation: Photometer Load the program called Photometer.vi from the chapter 6 program library. In this simulation, one explores the 555 monostable as a light transducer (light is converted into a time interval). Recall that the on-time is directly proportional to the magnitude of the external resistor and capacitor. The charging resistor is replaced with a photoresistor. The on-time (1.1RC) is then a measure of the input light intensity . In this demonstration, the light intensity can be varied from 0 to 10 lux. Investigate the relationship between light intensity and Ton. Click and drag the Light Intensity vertical slider marker. To make a measurement click on the Trigger switch.

Figure 7-5. LabVIEW Simulation - Monostable Circuit to Measure Light Intensity

LabVIEW Exercise Plot a graph of the photoresistance as measured from Ton versus the light intensity on a linear scale. Hint: Convert the lux scale into a linear scale.


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Lab 7


LabVIEW Simulation: Angular Displacement Transducer In the early days of consumer electronics, the Apple II microcomputer used a 555 timer chip to read angular position of a game paddle. Whenever the software instruction INP(0) or INP(1) was executed, a 555 timer chip on input 0 or input 1 was triggered. An internal capacitor with an external potentiometer in the game paddle was used to read the angular position of the game paddle knob. When the paddle was rotated, a new resistance was set. The on-time of the 555 output was measured by counting the number of instruction cycles from the start of the trigger pulse until the monostable returned to the off state. The span was scaled from 0 at one end to 255 at the other end. The angular resolution was approximately one degree per count. It was used to play numerous computer games. With a game paddle on each input, two could play games or the paddles could be used together to plot points on an XY graph such as “Etch-a-Sketch”.

LabVIEW Simulation: X-Y Joystick Load the program called XYJoystick.vi from the chapter 7 program library. The two game paddles are simulated using two LabVIEW virtual slide wires. Moving the slide causes a change in the resistance. For fixed capacitors, the on-time is then directly proportional to the resistance or angular rotation of the virtual knob. Two identical circuits have been provided so that both the X and Y motion of a cursor can be controlled. Note the variation in Ton for each channel as the slides are moved. The on-time is scaled to produce a number from 0 to 255.


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Figure 7-6. LabVIEW Simulation - Joy Stick Operation Using a Monostable Circuit

LabVIEW Challenge: Capacitance Meter Design a LabVIEW simulation to demonstrate how a 555 Timer IC can be used to measure capacitance. Hint: The capacitance is unknown and can vary over many decades. Choose a series of resistors of the same mantissa but different multipliers. For example: 1 kW, 10 kW, 100kW etc.

eLab Project 7 Objective To study the application of a 555 Timer IC in a triggered alarm circuit.

Procedure Build a monostable circuit based on the front Alarm.vi, Figure 7-4. Connect a 330 Ω resistor and red LED to the output (pin 3). Set R = 5.0 MΩ and C = 1.0 µF. A pushbutton is used as the triggering device. Each time the trigger is pushed, the output (pin3) goes low for a specific period of time. In order to invert the 555 output, a TTL buffer chip 7406 has been added. Its output (pin 4) now only goes high when the switch is triggered and stays high for the time set by the monostable circuit. The component layout is shown below.


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Lab 7


Figure 7-7. Component Layout for Triggered Alarm 555 Timer Circuit

Note 7406 is a TTL Hex Inverting Buffer, Input for Inverter No.2 is pin 3, Output for Inverter No.2 is pin 4, Power +5 volts is pin 14 and Gnd is pin 7.

Computer Automation 7: Measuring Time Interval The monostable circuit of eLab 7 produces a pulse of fixed length each time the 555 timer IC is triggered. All information about the circuit is contained within the pulse length. In this lab on computer automation, a time interval counter is used to measure the pulse width. Launch the program Pulse Width.vi from the program library of chapter 7. Note that some connections are require on the output of the DAQ card. Connect the output of counter0 to the clk or source input of counter1. Connect the output pin 3 of the 555 timer chip to the gate input of counter1. If you are using the DAQ card with the AMD9513 or DAQ-STC counter/timer chip, then use Measure Long Pulse Width.vi from the AMD9513.llb or DAQ-STC.llb library. Note

Pulse Width.vi has a variable time limit. If during this time a pulse is detected then the pulse width is measured and the VI stops. If no pulse is detected, the VI stops after the time limit and a Boolean LED display is lite. Set the time limit to at least 10 seconds.


7-9



Run the program by clicking on the Run button. With the program running, now generate a trigger signal by momentarily pressing on the push button of eLab 7. Pulse Width.vi will report on a front , the width of the pulse generated by the 555 monostable circuit. Observe how the measurement accuracy depends on the timebase.

Circuit Enhancements Replace the resistor with a variable resistor in the range 10–100 kΩ, and investigate the changes in pulse width as the resistance is changed. Replace the capacitor with a variable capacitor in the range 0.05–1 µf, and investigate the changes in pulse width as the capacitance is changed.

LabVIEW Enhancements Design a LabVIEW program which continuously monitor the 555 monostable circuit and reports the pulse width of each pulse generated by the trigger signal.


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Lab 8 Voltage-to-Frequency Converters Historically, voltage-to-frequency (V-F) converters were used as the input stage for digital recorders. A slowly varying input analog signal was converted into a frequency, then recorded on a conventional magnetic tape recorder. This combination provided a high precision analog recorder, whose output was a digital frequency. More recently, V-F converters are found in the front end of inexpensive digital voltmeters, and other low cost analog-to-digital circuits. The classic 555-timer chip studied in Lab 7 is a form of voltage-to-frequency converter. The heart of a V-F converter is an integrating op-amp circuit. The input voltage is connected to the integrator, which ramps up to a preset voltage level. At this upper limit, the input is replaced with a reference input, but of the opposite polarity, and the output integrates down to a lower limit. At this limit, the reference input is removed and the input signal reconnected. The oscillator cycle begins again. The output is a logic low during signal integration, and a logic high during reference integration. The resulting waveform has constant on-time, and a variable off-time, proportional to the magnitude of the input signal. The output frequency is proportional to the input signal level. A V-F converter consists of four fundamental op-amp building blocks: an electronic switch, an integrator, a comparator and a monostable.

Vin

C

Vref

Switch

Integrater

Comparater

MS

Vout

Monostable

Figure 8-1. The Building Blocks of a Voltage-to-Frequency Converter


8-1


Lab 8 Voltage-to-Frequency Converters

The input Vin (usually a negative voltage) is ramped up by the op-amp integrator. In the following example, the output rises from –10 volts towards 0 volts. An op-amp comparator is referenced at zero volts. At this upper limit, it switches from a high state to a low state creating a negative going pulse used to trigger the next stage, a 555 monostable. Once triggered, the output of the monostable (a positive voltage) replaces the input voltage. The integrator now ramps down until the monostable has timed out. The monstable voltage is replaced with the input signal and the cycle begins again. In the following diagram, the input voltage is –5 volts. The upper reference level is 0 volts and the lower reference level is set by the monostable on-time. The capacitor voltage is shown as the heavy (red) trace. The monstable output goes from 0 to 5 volts (yellow trace). The comparator output is seem as the light line (green trace) which goes from +15 to –15 and back to +15 volts.

Figure 8-2. LabVIEW Display of the V-F Timing Diagrams

Reducing the input signal lowers the charging rate (slope of the heavy line), increasing the period and decreasing the frequency.

Block 1: The Op-Amp Integrator When a capacitor is placed in the loop of a conventional inverting op-amp circuit, the result is that the summing current is accumulated on the capacitor. The output voltage thus becomes the sum of all the input charges.


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Lab 8

Voltage-to-Frequency Converters

C R A +

V in

V out

Figure 8-3. Op-Amp Integrator Circuit

From Lab 2, you will recall that the output voltage is the integral of the input voltage scaled by the charging time constant RC. Vout = - 1/RC ∫Vin dt

(8-1)

If the input voltage is a constant and negative, the output voltage becomes a ramp increasing linearly until the output reaches the positive rail voltage. If you reverse the input voltage, the op-amp integrates downwards linearly until it reaches the negative rail. The ramp output is just Vout = - (Vin/RC) t

(8-2)

In order to simulate the operation of the V-F circuit, time is divided into time slices and the differential form of the above equation is used to calculate the output voltage V'out at the end of each time slice: V'out = Vout - (Vin/RC) ∆ t

(8-3)

where Vout is the voltage at the start of the time slice and ∆t is the size of the time slice.

LabVIEW Demo 8.1: Operation of an Op-Amp Integrator Load the program called Integrator1.vi from the chapter 8 library. This program simulates the dynamic operation of an op-amp using Equation 8-3. Each time you click on Run, a new output voltage is calculated and displayed on a chart (capacitor voltage versus time). Initially the output voltage is set to –3 volts. With Vin = –5 volts, R = 150 kΩ and C= 0.1µf, the incremental voltage will be 0.333 V for a 1 millisecond time slice. Click the run button a few times so you can see the ramping voltage. At any time, you can change Vin, R or C to modify the rate of change (the slope of the ramp). In fact if you change the sign of the input, the output voltage will ramp down.


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Try clicking on the run button 10 times. Then change the sign of the input voltage. Again click the run button 10 times. What kind of waveform have you just generated?

LabVIEW Project A Real Op-amp Integrator Use a real op-amp (741) to build the integrator circuit below.

150 k Ω

0.1 µF

A +

V in

V out

Figure 8-4. Op-Amp Intetgrator Circuit with Manual Reset

Apply a 2 volt P-P, 100 kHz square wave to the input. Observe both the input and output signals on a dual channel oscilloscope or DAQ card. Observe what happens if the signal amplitude becomes too large. What happens when the frequency becomes too small at a constant amplitude. What do you think will happen if the input signal is a triangular waveform? Try it!

Block 2: Comparator An op-amp with no input resistor and no resistor becomes a comparator. If the signal on the summing input (–) is larger than the non-inverting input (+), then the output swings to the maximum negative voltage. If the signal at the summing input is smaller than the non-inverting input, then the output swings to the maximum positive voltage. The speed of the change from one rail to the other is related to the open loop gain and is called the slew rate. By connecting a reference voltage (Vref) to one of the inputs, a trigger level can be defined at Vref and a negative-going output will signal when the input voltage is larger than the reference voltage.


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Lab 8

V in V ref


A +

V out

Figure 8-5. Op-Amp Comparator Circuit

LabVIEW Demo 8.2: Op-Amp Comparator in Action Load the program called Comparator1.vi from the chapter 8 library. Run the program and observe that the comparator output can only be at one or the other rail voltage. In the V-F circuit, the reference voltage will be taken as zero volts. Modify the reference voltage to this value and run the VI again.

LabVIEW Demo 8.3: Op-Amp Integrator and Comparator in Series Load the program called Integrator2.vi from the chapter 8 library. Each time you click on Run, a new output voltage is calculated. Initially the integrator voltage is set to –3 volts. As before with Vin = –5 volts, R = 150 kΩ and C= 0.1µf, the incremental voltage for each 1 millisecond time slice will be 0.333 V. Watch the comparator output when the integrator reaches the reference voltage at zero volts. Continue clicking until the integrator output reaches +3 volts. Now reverse the input voltage to +5 volts and integrate down through the reference voltage until the integrator output is –3 volts. Repeat the cycle (Vin = –5 v, 10 clicks; Vin = +5 v, 10 clicks) once more. The sign of the comparator output signals when the input is positive or negative. Notice that the comparator changes state or is toggled each time the integrator level crosses zero volts. In this mode, the comparator is a zero crossing detector. Notice the waveform produced on the integrator and comparator outputs. In the V-F circuit, the reference voltage will be set to zero volts (upper limit) and the lower limit (initial voltage) will be set to some negative voltage.

Block 3: The Monostable Recall from Lab 7 that when a 555 monostable is triggered, the output goes high for a period of time set by an external resistor and capacitor. The on-time is 1.1 RC. Setting R = 36 kΩ and C = 0.1 µf yields an on-time of 3.96 milliseconds. The monostable needs a falling edge to trigger the circuit, followed by a rising edge. This is accomplished in the real V-F circuit using a resistor-diode network consisting of a 1.5 kΩ resistor and two 1N914 diodes used to clamp the trigger voltage within the 555’s input range.


8-5



R

+1 5 V

C R = 36 kΩ

1 .5 kΩ

Vi n

C = 0.1 µf

555 t rig Q

1N914

Vout

MS Figure 8-6. 555 Monostable Circuit

The monstable output when high will be close to the positive power supply voltage and will be used to forward bias a third 1N914 silicon diode shown in the next section. A high output allows current to through an 0.5 kΩ output resistor to ground. From Ohm’s law, this current will be (15.0 V-0.6 V)/0.5 kΩ = 28.8 ma.

LabVIEW Demo 8.4: Monostable Operation Load the program called Monostable.vi from the chapter 8 program library. Click on the Run button to activate the circuit and click on the trigger switch to trigger the monostable.


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Lab 8


Figure 8-7. LabVIEW Simulation – Monostable Circuit as a Current Driver

Note that current only flows through the resistor when the monostable is triggered. The magnitude of the current can be adjusted with the choice of the resistor. Question: Suppose the above current was used as the input to the integrator, how long would it take the integrator voltage to reach –10 volts assuming that the output voltage was initially 0 volts? The answer is contained in Equation 8-3. V'out = Vout - (iin/C) ∆t

or

-10 = 0 - (28.8 ma/0.1µf) ∆t

∆t = 34.7 microseconds

(8-4) (8-5)

Part 4: A Real V-F Converter The output of the monostable is used in a real V-F converter circuit to generate a reset current for the integrator. When the diode is forward biased by the monostable, a reset current is applied to the summing point of the integrator. Since the monostable current is much larger than the input current, the summing point becomes the switch and the integrator is ramped down for a time defined by 1.1RC. When the monostable shuts off, the input current dominates and the integrator output ramps up to 0 volts. Here the


8-7



monstable resets and the cycle starts again. The period as seen on the monostable output is related to the input voltage level. When the monostable on-time is short, the frequency is directly proportional to the input voltage, a true V-F converter.

0.1µF

R

+15 V

Vin

C

150 kΩ +

A

+

A

1.5 kΩ trig 1N914

555

Q

Vout

MS 0.5 kΩ

1N914

Figure 8-8. 555 Schematic Diagram for a Real V-F Converter Circuit

LabVIEW Demo 5: Operation of the V-F Circuit Load the program called VF.vi from the chapter 8 program library, VF.llb. Click on the Run button and investigate the variation of the period with the input level. When the action is stopped, the magnifying cursor can be used to expand the time to see a close up of the complete timing diagram.

Figure 8-9. V-F Timing Diagrams


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Lab 8


When the monostable is off, the input signal (red trace) ramps up until the integrator output reaches the comparator trigger level at zero volts. The comparator (green trace) flips to the opposite rail generating a trigger signal for the monostable which in turn (yellow trace) generates a reset current that is much larger than the input signal and of opposite sign. The integrator ramps down towards a negative voltage. As soon as the integrator voltage reaches zero volts, the comparator flips back to its initial state (+15 V). At the end of the monostable timing period, the reset current is returned to zero and the integrator ramps up again driven by the input signal level.

LabVIEW Exercise Plot the output frequency versus input voltage.

eLab Project 8 Objective To study the operation of a Voltage-to-Frequency converter circuit built from basic analog chips, the op-amp and the 555 timer.

Procedure Build a voltage-to-frequency converter circuit using the schematic diagram of Figure 8-8. It requires four resistors, two capacitors, three silicon diodes, two op-amps and one 555 timer IC. The chip pinouts can be found in Lab 1, Figure 1-5 and Lab 6, Figure 6-1. The op-amps and timer chips are powered from +15 and –15 volt power supplies. The circuit requires that the integrator be in a known state (a negative or zero voltage on the input) for the to work correctly. This is easily set be momentarily shorting the integrator capacitor. After started the circuit will run until the power is removed. The component layout is shown below.


8-9



Figure 8-10. V-F Component Layout

Plot the V-F output frequency as the input voltage in varied from –5 to –0.5 volts.

Computer Automation 8: V-F Calibration Curve Computer Automation implies the repetitive measurement of circuit parameters and the analysis and reporting of that data set. In this lab, a system test for the V-F circuit of eLab 8 is presented. The operator will be able to set a range of test input signals and the number of tests to be run. In operation, a test voltage is output on one pin of the DAQ card which is to be connect to the input of the V-F circuit. The V-F output can be connected to a counter input pin of the DAQ card and using Frequency.vi, introduce in computer automation lab 6, the frequency of the V-F circuit measured. After all data points are collected, the V-F calibration curve is displayed on the front .

LabVIEW Design A starting design for a LabVIEW test program, called V-F Scan.vi is found in the program library. Launch this program and open up the diagram window. Notice that two subVIs, Write1pt.vi and Frequency.vi are used. Write1pt.vi is a subVI used in earlier labs to generate a test voltage on the ana pin [device1/channel0]. Connect this pin to the input lead of the eLab V-F circuit. Frequency.vi is similar to FrequencyLow.vi introduced in


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Lab 8


the computer automation lab 6, but modified so that it can be used as a subVI. Connect the output of the eLab V-F circuit to counter2 clk input pin of your DAQ card. Select the start and stop voltage levels and the number of points to acquire for the calibration curve. When all wires are connected and the V-F circuit is operating, click on Run. Each input voltage level and measured frequency will be displayed as it is measured. After all n points have been acquired, the calibration curve will appear in the graph display.

LabVIEW Enhancements Design a LabVIEW program that fits a polynomial curve to your measured calibration curve and displays the polynomial coefficients.


8-11


Lab 9 Nonlinear Circuits: Log Amps In the days before slide rules, calculators and computers, complex mathematical functions such as division, square roots and powers were solved using logarithmic tables. Two of the most common properties of logarithms reduced multiplication and division to addition and subtraction. These are Log(AB) = Log(A) + Log(B) Log(A/B) = Log(A) – Log(B). We have already seen in Lab 2 how summing and difference op-amp circuits can add and subtract. Provided a log op-amp circuit exists, the above relationships can be used to build multiply and divide circuits. The diode introduced in Lab 3 displays a nonlinear response in the current-voltage characteristic curve. When forward biased, the diode current is exponentially related to the voltage across the diode. Id = io exp(Vd/a)

(9-1)

where io is the reverse bias diode current (a constant) and a= kT/e. Solving for V yields a natural logarithmic relationship between the voltage across the diode and the current ing through the diode. Vd = a loge (Id/Io)


9-1

(9-2)


Lab 9 Nonlinear Circuits: Log Amps

Log Op-Amp Circuit A log op-amp circuit can be build by replacing the resistor of the inverting amplifier with a diode.

D

1 00 kΩ -

Vi n

R1

+

V out

(Note: Vi n is -)

Figure 9-1. Schematic Diagram of an Op-Amp Logarithmic Circuit

For the input loop, the current is i1 = Vin/ R1

(9-3)

For the loop, the current if is Id and Vout is Vd

(9-4)

At the summing point i1 = - If

(9-5)

Together these equation are i1 = Vin/R1 = - if = -Id = - io exp(Vout /a) (9-6) and solving for Vout yields Vout = a loge (Vin/ io R1)

(9-7)

With the careful diode selection, this expression is valid over 5 - 6 decades. Diodes such as 1N914 and some common transistors (2N3900A) with the base and collector pins tied together, work well. The constant “a” is about 0.059 volts at room temperature and io is typically 10-11 amps.

LabVIEW Demo 9.1: Log OpAmp Circuit Load the program called LogOpAmp.vi from the chapter 9 program library. Click on the Run button to activate the circuit. Investigate the output voltage as the input is varied over five decades of voltage levels.


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Lab 9

Nonlinear Circuits: Log Amps

Figure 9-2. LabVIEW Simulation - Op-Amp Logarithmic Circuit

This VI is an exact op-amp simulation of Equation 9-7 using the typical values for “a” and io. To convert the input voltage (1.000 volt) into the natural logarithm for 'one', requires that the output be scaled so that loge (1 volt) does in fact yield the numeric value ln(1) = 0.000. A second program entitled Ln.vi scales the output of LogOpAmp.vi to generate the correct natural logarithm values. A further scaling is required to convert the natural logarithm base(e) into the normal logarithm base(10). A third program LogN.vi further scales LogOpAmp.vi to demonstrate how a input voltage is converted into a numeric log value. The scaling and conversion factors are found in a subVI called Scaling.vi. It uses the op amp circuits for subtraction and multiplication by a constant found in Lab 2.

An Analog Decibel Calculator Many analog measurements require that a signal be measured in decibels. Recall from Lab 4, a decibel is defined as N(dB) = 20 log(Vout/ V0) where V0 is a reference voltage. One can use two log amps and the difference circuit from Lab 2 to build an analog decibel conversion circuit.


9-3



D

R1 V

+

R* R -

Vout

+

R

D

R1 Vo

R*

+

Figure 9-3. Schematic Diagram of an Op-Amp Decibel Analog Calculator

The op-amp circuit shown above calculates the logarithmic ratio log (V/Vo). This is a common calculation used in many applications especially in photometery. By replacing the resistor R* with 20 R, the above circuit calculates decibels. The equivalent LabVIEW simulation for the decibel calculator uses two log amps, a difference function and a multiplication by 20. The following figure shows the strong similarity of the LabVIEW simulation (diagram page) with the schematic diagram (Figure 9-3) for an op-amp decibel calculator.

Figure 9-4. LabVIEW Diagram of an Op-Amp Decibel Calculator


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Lab 9


LabVIEW Demo 9.2: Decibel Calculator Load the program called Decibel.vi from the chapter 9 program library. Enter the output voltage and the reference voltage. Click on the Run button to execute a calculation. If V is the output voltage and V0 is the reference voltage for this op-amp circuit, then the calculation gives the gain in decibels.

Exponential Op-Amp Circuit You may have noticed the symmetry of interchanging a special component between the and input loop. For example, a capacitor in the loop yields an integrator while a capacitor in the input loop yields a differentiator. Diodes also have this symmetry property. A diode in the loop yields a log amp circuit while a diode in the input loop yields an exponential circuit.

Rf if

i1

Vi n

100 kΩ -

D

V out

+

(Note: Vi n is +)

Figure 9-5. Schematic Diagram of an Op-Amp Exponential Circuit


For the input loop, the current is i1 = io exp(Vin /a)

(9-8)

For the loop, the current is Vout = - if Rf

(9-9)

At the summing point i1 = - if

(9-10)

Together these equations are io exp(Vin /a) = i1 = -if = Vout /Rf

(9-11)

Vout = io Rf exp(Vin/a)

(9-12)

9-5



This circuit provides the antilog or exponential function which can be used to convert a log sum or difference back into simple numbers. AntiLog {Log(AB)} = AB

(9-13)

AntiLog {Log(A/B)} = A/B

(9-14)

Notice that the previous op-amp circuits when followed by the antilog circuit provides the function multiply or divide.

Analog Multiplication of Two Variables Multiplication of two variable signals X and Y can be accomplished with the help of Equation 9-13. It is expanded to read AntiLog {Log(X)+LogY)} = AntiLog {Log(XY)} = XY

(9-15)

First one calculates Log(X) and Log(Y) using the Log op-amp circuit. Then these are added together with the summing circuit from Lab 2. Finally the exponential of the resultant voltage is computed using an anti-log op-amp circuit. For noise reduction, the output is often reduced by a factor of ten. The schematic diagram for the circuit op-amp circuit follows

D1

R1 X

+

1 R

R1 /10

R +

D2

R1 Y

3

-

E3

+

4

XY/10

R

+

2

Figure 9-6. Op-Amp Circuit for the Multiplication of Two Variables

LabVIEW Challenge Design a LabVIEW program that simulates the analog multiplication circuit shown above. Make good use of the Lab 9 program library and sub-VIs to produce a compact program.


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Lab 9


Raising and Input Signal to a Power Many physical laws follow a simple power law and a circuit that can raise an input signal to a specific power (possibily a fraction) is of great use. The op-amp circuit makes use of the logarithm property to raise an aput X to a constant power y. AntiLog {y Log(X)} = AntiLog {Log(Xy)} = Xy

(9-16)

First one calculates Log(X) using the log op-amp circuit. Its output is multiplied by the constant (y) using the inverting op-amp circuit from Lab 2. Finally the exponential of this voltage is computed using an anti-log op-amp circuit to give the final result Xy. The electronic schematic circuit for the power law follows. yR D1

R1 X

-

R

1

+

-

R1 D3

2

-

+ +

3

-X

y

Figure 9-7. Schematic Diagram of an Op-Amp Power Law Circuit

Note that a resistance potentiometer with one lead shorted to the wiper lead is used to set the Gain of the second op-amp (G = yR/R) to y. The fraction y can be an integer number, half integer or any other fraction.

LabVIEW Challenge Design a LabVIEW program that simulates the raise to a power op-amp circuit shown above. Make good use of the Lab 9 program library and sub-VIs to produce a compact program.

eLab Project 9 Objective To study the operation of an op-amp logarithmic circuit.

Procedure Build a log amplifier using the schematic diagram of Figure 9-1. It requires a resistor, a silicon diode, a 741 op-amp. If a silicon signal diode is not available, a transistor such as a 2N3900A with the base and emitter lead tied together works well. A small 0.001 µF capacitor is placed across the diode


9-7



to suppress noise. The op-amp is powered from a +15 and a –15 volt power supply. The component layout is shown below.

Figure 9-8. Component Layout for Op-Amp Log Amplifier

Investigate the operation of the logarithmic op-amp circuit by applying a variable amplitude DC voltage to the input pin 2. Plot the output voltage as a function of the input voltage on both a linear and logarithmic plot. How well does the circuit work for AC input signal levels?


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