Lab 4 - EE 420L 

Steven Leung

2/24/15

leungs@unlv.nevada.edu 

  

Pre-lab work

 

 
Introduction - This lab deals mainly with the concept of bandwidth versus gain of different op amp configurations and slew rate of an op amp. The gain times the bandwidth of an op-amp is a constant value and it can be seen that as gain increases, the bandwidth will decrease. We consider the bandwidth of an op-amp configuration to be the frequency from 0 to 3db beuccase the op amp fall at a rate of -20db/decade. 3db frequency is the frequency when the output is .707 of the input. Slew rate relates to how fast the op amp output can change, for example, a square wvae  ideally changes from 0 to Vpeak instantaneousy but we know that practially, nothing can change insteantaneously so then the chagne will be delayed. Slep rate is measured in the number of volts the output can change per seconed.

Experiment 1     Estimate, using the datasheet, the bandwidthfor non-invertying op-amp topoliges having gains of 1,5,10.
 

    Open loop Frequency response of LM 324 (Figure 1)
 
From the figure above (figure 1), it can be seen that for a gain of 1 (0db) the bandwidth will be about 1Mhz. For a gain of 5 (~14db) is just over 100K so we can estimiate it as about 300 Khz. Lastly for a gain of 10 (20db), it can be seen that the bandwidth will be about 100Khz.
 
 Experiment 2    Experimentally very these estimates for non-invertingop-amp topologies hving gains of 1,5,10.

               
                   Non-inverting with gain of 1 (Figure 2)                                                                       Non-inverting with a gain of 5 (Figure 3)
 
To test the bandwidths of of the LM 324 op amp with the specified gains we built the circuits in figure 2 and figure 3. Figure 2 includes a non inverting gain of 1 (which is the same as a voltage follower). Figure 3 shows a non inverting op-amp with a gain of 5. The formula for non-inverting op-amp topology is Vout/Vin=1+Rf/Ri. To measure the bandwidth of a non inverting gain of 10 is done by a similar circuit to figure 3 but Rf will be 900K instead of 400K (becuase 1+900K/100K=10). The simulation results are shown below.

                           

                 Non inverting W/ gain 1 (figure 4)                                   Non inverting W/gain 5 (figure 5)                                                   Non inverting W/gain 10 (figure 6)

 

For the above experiments, we used the 3db corner frequency to measure the bandwidth of the different gains. For a gain of 1, when the output is about 70 mv (.707*1mV), the frequency at that value will be the 3db frequency in which this case it is around 670KHz. For the gain of 5, when the output is .707mV (.707*1V), that will be the value of the bandwidth which in this case is 106KHz. For the gain of 10, when the output is 1.41 (.707*2V), that will be the value of the bandwidth which is 40KHz. Notice that these values are a little lower that the ones approximated form the data sheet. The reason for this is beucase the values on the data sheet are for when the supply voltage on the rails of the op-amp is 30V but for this experiment we are only using 5V. If a 30V rail were to be used, our results will match closely to the datasheet (see figure 7).  Figure 7 shows a gain of 1 with a noninverting op-amp at 1MHz. It can be seen that for this case the op-amp operates fine at 1Mhz compared to figure 4 where even at 600KHz, the output is reduced. One might say that in figure 7 there is still a gain of 1 at 1Mhz which would mean that the 3db cornor frequency is going to be higher (until the output is 141mV). The reasoning for this is that the values on the data sheet are esimates and if we increase the frequency of figure 7 a little we wil see the output fall to 141mV quickly. Therefore the same idea applies for the gains of 5 and 10, if we used a Vcc of 30 volts, we will get closer simulations to that of the datasheet. 

 

            Non inverting gain 1 W/ 30V rail (figure 7)

 

Experiment 3     Repeat experiment 2 using the inverting op-amp topology having gains of -1,-5,10. 

 

                   inverting gain of 1 (figure 8)

 

Figure 8 shows the circuit for a inverting gain of -1. The formula relating input and output for an inverting op-amp is Vout/Vin=-Rf/Ri. From this equation we can modify the circuit in figure 8 to simulate a gain of -5 and -10. For a gain of -5 we changed Rf to be 500K and for a gain of -10 we changed Rf to be 1MEG. The simulation results are shown below. 

 

       

                    Inverting w/Gain 1 (figure9)                                                                   Inverting w/Gain 5 (figure 10)

   

 

 

                    Inverting w/Gain 10 (figure 11)

 

Calculating the 3db corner frequency for the inverting topology is exactly the same as the noninverting (frequency when Vout=.707*Vin). From figure 9 the 3db frequency of a gain of -1 is ~650KHz. From figure 10, the 3db frequency of a gain of -5 is ~87K. From figure 11, the 3db frequency of a gain of -10 is ~33KHz. The estimations of these gains from the data sheet are the same as the estimations for the non-inverting topology, the negative sign from the inverting topology just represents a phase shift which can be seen in each of the figures 9-11. It can also be seen that the 3db frequencies of the corresponding gains from the non-inverting topology to the inverting topology are similar. The reason why these results are not exactly the same as the data sheet are also the same, beucase the data sheet simulates the op-amp with a 30V rail and we are using a 5V rail. Increasing the rail voltage, will yield better resutls. 

 

Results 

Approximation Non-inverting topologyinverting
1 or -11MHz650KHz
5 or -5300KHz106KHz87KHz
10 or -10100KHz40KHz33KHz

Experiment 4    Design two circuit for measuring the slew rate of the LM324, one circuit should use a pulse input while the other should use a sinewave input.

 

For the most part, we used the same circuit to measure both the slew rate of a pulse and sinewave input. We used the inverting topology with a gain of 10 with the input being at a higher amplitude, similar to figure 8 (but with a gain of 10). The reason why we choose a higer gain than for example 1, is that with a larger gain, there is a larger change in voltage in a larger time, therfore we can get a more accurate measurment.The slew rate of a circuit depends on both the amplitude and frequency of the circuit becuase the slew rate can be achieved by increasing one or the other (or both), therefore by increasing both, we can generate the maximumin slew rate with a reasonable input signal. Since we are using a higher amplitude in the input, we will have to increase our rails so that our circuit will not saturate. For this experiment, we increased our rail to 15 V.

 

For the square wave input as seen in figure 12, we can see the output slewing when the input is 720mV at a frequency at 420KHz. The slew rate being defined as the maximum change in voltage per unit time can be calculated by dividing the peak to peak voltage by the rise time (452mV/876ns=.52V/us).This means that the maximum voltage change in this circuit is that the output can change about .5 volts every microsecond. The data sheet value for this op-amp is .4V/us. The circuit in figure 12 slews becuase the input square wave changes from the pos peak to the negative peak quicker than the slew rate can respons, therefore when the output is tring to go high becuase the input went high, before it can reach that peak voltage, the input is now low and it trys to go to the low voltage. This process repeats and the output will never go to either the high or low voltages of the input. By increasing the frequency or amplitude, the slew rate will not change significantly becuase of the fact that it depends on both frequency and amplitude. If we were to increase the amplitude, nothing should change becuase this will just be increasing the voltage that the output can never reach anyway but the amplidtude will matter if it were to be decreased. If we were to increase the frequency, that will make the peak to peak value smaller becuase it will give less time for the output to respond but at the same time, the rise time sill also be decrease which means that the two effects would cancel each other out. 

 

                       

                Slew rate of square wave input (figure 12)                                                            Slew rate of sine wave input (figure 13)

 

The same idea is applied to the sine wave input of why we chose the gain and amplitude of the input, so that we can achieve the max slew ratethrough a reasonable input. The slew rate of a sine wave input to the LM324 op-amp (figure 13) is .69V/uS (184mV/265nS=.69V/uS).

 
There is only a small difference between the readings off the data sheet versus our experiment. The reason for this is that the .4V/uS value on the datasheet is just a typical value, every LM324 can have a slightly different slew rate. A reason why the slew rate of the square wave input versus the sine wave input do not match is beucase maybe on the square wave input, we are off to the max slew rate by a little, meaning that we can still increase the frequency slightly to get a higher slew rate.
 
 Conclusion
The main lesson I learned from this lab is the effect of high frequency on circuits and the tradeoff between gain and frequency. If you wanted a higher bandwidth, you will have a lower gain and if you want a higher gain, you will have a smaller bandwidth. In addition, frequency will not only reduce the gain of your circuit but when mixed with a high input ac amplitude, the circuit will not fucntion if it gove above the slew rate meaning that the op-amp or circuti is not build to handle the speed that you are using for it.

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