Lab 4 - ECE 421L 

Authored by Nicholas Banas,

Banasn1@unlv.nevada.edu

2/23/15 

  

This lab covers the gain-bandwidth product and slew rate of op-amps.

Op-amp LM324 Non-Inverting Bandwidth 

 The bandwidth of the LM324 in the non-inverting configuration can be calculated by using the GBP (Gain Bandwidth Product) of the chip with the closed loop gain of the circuit design.  From the data sheet the GBP is:
 

 
While the GPB will vary somewhat with different circuit topologies, this is a good ballpark estimate for these calculations.  The calculations boil down to GBP/Acl=BW.  The base bandwidths for our non-inverting topologies are 1x=1.3MHz, 5x=260kHz and 10x=130kHz.
 
 

 
Using a spice model for the LM324 we can calculate the values of the 3dB BW for the different topologies:
 

 
You can see from the measurements that BW1x is 882kHz, BW5x is 148kHz and BW10x is 66kHz.  These are significantly lower than the estimates from the data sheet.  We'll take some real measurements and see which is closer.  A quick note on the x1 measurement, the spice sim for 1x seems to have an issue around 700kHz that makes for inaccurate data.  I took the measurement from 0dB instead of -3 as it seems to be very close to where the -3dB should be.
 
 
  The Bode Plot above illistrates how the output decreases at a steady rate after the 3dB BW has been reached.
 

1x Amp at 3dB5x Amp at 3dB10x Amp at 3dB
 
The real world measured results are fairly close to the sim results. The measurements seem to suggest that the GBP is closer to ~700kHz.  

Variations in the LM324

So why does the data sheet have such a high GBP.  Well the data sheet also lists the test condidtions that the chip was under to measure the GBP listed.  The largest difference in our setup from the listed conditions is the Vcc.  Lets retake the measurements at 1x gain with 30Vcc and see the differences.
 
5V Vcc30V Vcc
 
You can see the difference is significant.  It appears that the 3dB frequency should be much closer to 1.3MHz now.
 
5Vcc 3dB Frequency30Vcc 3dB Frequency

The 3dB frequency is now 1.1MHz, much closer to the 1.3MHz listed.  While the chip is able to be operated at small Vcc's, they appear to effect the performance significantly.


The Inverting Amp

We created a basic inverting amplifier using the following schematic.
 

 
 The calculations for the inserting topologies are slightly different, with the equation being GBP/(1+R2/R1)=BW.  So our estimates are -1x=650kHz, -5x=220kHz and -10x=120kHz.
 

 
These calculations differ again.  The -5x and -10x can be explained by the reduced Vcc, but the value for the -1x seems to imply that the BW should have been estimated with GBP/ACL=BW.  We will see what the real world measurements are.  
 
 

 

Once again, the bode plot shows the decline in the BW over higher freqencies.  The -1x seems to have worked correctly this time.

 
-1x Amp at 3dB-5x Amp at 3dB-10x Amp at 3dB

  
   The lab measurements show 3dB frequencies of: -1x=813kHz, -5x=120kHz and -10x=55kHz.  The values for -5x and -10x are very close to the sim while the -1x is actually higher than the sim.  Once again, these values seem to suggest that the correct calculation should be GBP/-Acl=BW.

Measuring the Slew Rate

 We designed the following circuit to measure the slew rate of the LM324.
 

 
The sim plot shows the response to a sine input.  You can see how the output can not keep up with the input.  While there is some error due to the turn around response, it is a very close estimate to just use (voltage increase)/(rise time) to get the V/us  value for the slew rate.
 
  
 
Testing the in the lab shows that the circuit seems to work as designed.  With a voltage rise of 1V and a rise time of 2.2us, the measured slew rate is ~.45 V/us.
 
 
 
We are able to use the same circuit with a pulse input.   
 
 
 
The graph shows a similar result to the square input as with the sine input.
 
 
 
 The lab measurement shows an even nicer output with a smaller effect from the turn around.  The measurments with the square wave are 1V over 2.15us.  This shows a slightly higher slew rate of .465 V/us.
 
 
 
From the data sheet:
 


 This is very close to our measured value.  This is because we used a similar setup to the one used for the calculations.  Not show in our schematics is a 5k load resister that we inserted after we started the test. The measurements without the resistor were very inaccurate, with almost no slew restriction.  This is because the slew limit is strongly influenced by the current sourced/sunk by the op-amp.
 
  A note on the difference between the square and sine inputs: while the same setup can be used for both inputs, the frequency or input voltage for the sine must be much greater.  Measurements in the lab the lab seem to indicate that the minimum V*f of the sine input must be about 4 times larger than the square input for usable results.  We were able to use the same setup because we used the min values for the sine for both inputs.