Lab 3 Op-Amps I, basic topologies, finite gain, and offset - EE 420L 

Authored by Jeremy Garrod  

02/15/2017
Email: garrod@unlv.nevada.edu

  

Pre-Lab Work

 

Pre-lab work



Lab Work

The data sheet states that at +25ºC the minimum VCM is 0v and the maximum VCM is Vcc - 1.5V = 5V - 1.5V = 3.5V in the case of this experiment. The maximum Vcc that is allowed is +30V.

 


The data sheet states that the open-loop gain is 100V/mV which is a gain of 100,000 or 100dB. The second image below shows that the open-loop gain is right around 100dB at 10Hz.








The data sheet states that a typical offset voltage for the LM324 is 2mV, so that is a good estimate of what to expect. For the worst case design, the maximum offset should be used. While at +25ºC, which is room temperature, the maximum offset voltage is 5mV the 9mV offset should be used when designing for the worst case scenario. This accounts for extreme temperatures as well as giving a nice buffer to the designer.





Build, and test, the following circuit. Note that a precise value for the 5k resistors isn't important. You can use 4.7k or 5.1k resistors.

fig1.jpg


The common-mode voltage is the voltage that is applied to both the inverting and non-inverting terminals of the Op-Amp. It should be 2.5V in this circuit due to the 2.5V offset on the sinusoidal source that is on the inverting termincal as well the fact that there is a voltage divider that outputs 2.5V to the non-inverting terminal. If everything was ideal, the VCM should not change. The voltage divider and sinusoidal source are both fixed and not variables. However, in reality there will not be an exact match between terminals due to variations in each source.


                        Voltage divider hand calculations


                              Output of voltage divider


Due to the inverting topology of the Op-Amp circuit, the ideal closed-loop gain is -1

                        
                 Ideal Closed-Loop Gain Hand Calculations

The output swing is the voltage range that is actually output by the Op-Amp. In this experiment, the swing is roughly 200mV and is centered around VCM which is 2.5V. Due to the inverting topology, the output will have the same amplitude as the input but 180º out of phase. This can be seen in an image below. If the input is not centered around VCM then the output can possibly clip. Since the swing is both positive and negative, if you go down too low you risk going under the 0V lower limit and clipping. If you go too high then you risk going above the 5V upper limit and clipping.


             Input and output waveforms showing a gain of -1


                 Waveforms when input is centered around 0V
Since the output swing is centered around 2.5V, the input signal amplitude can't be larger than 2.5V or else it will go over the 5V Vcc+ and clip as well as go under the 0V Vcc- and clip.


If we are increasing the gain to 10, that means that the input voltage will be multiplied by 10. In order to keep within the 2.5V input signal boundary, the input signal can't be larger than 2.5V/10 or 250mV or else it will be amplified past the supply voltage.


These capacitors are used to keep the DC voltage of VCM at a constant value. If any changes were to occur with the power supply, the capacitors will make up for the loss of voltage. They also filter out any AC noise that may come from the power supply or other sources since they act as a short to AC signals. This keeps a nice and clean DC signal going into the inverting terminal of the Op-Amp. The capacitances should be fairly large in order to act as a wire for AC signals. Other than that one condition, the values do not matter.



This bias current flows through R1 and R2 which the bias current sees as being in parallel. This current flow causes a a voltage drop, which actually increases our VCM voltage. In this experiment, R1 and R2 were both 10k. This would cause a voltage drop of 20nA * (10k||10k) = 0.1mV. This is a tiny voltage, so adding it to VCM doesn't do much. However, if the resistors were larger, such as 1MEG you would get a voltage drop of 20nA * (1MEG||1MEG) which creates a drop of 10mV. Adding this larger voltage to VCM would change the output of the circuit and possibly cause clipping. Sadly, I did not get a picture of the output of the circuit with larger resistors.

There is an input bias current that flows out of both terminals. If they are not equal, the difference is called the input offset current. For the LM324 Op-Amp, the input offset current can be seen in the image below.



Explain how the following circuit can be used to measure the op-amp's offset voltage.
fig2.jpg
In this circuit, the voltage divider provides the voltage to both terminals of the Op-Amp. If it was an ideal Op-Amp, there would be no current flow, which means that VCM and VM have the same voltage. However, if there is an offset then Vm and VCM would not be equal,. The offset of the Op-Amp would be added to VCM, making VM = VCM + Voffset. This offset will then be amplified by the gain of the inverting amplifier and added to the output voltage. So, in order to measure the offset voltage, take the output voltage and subtract if from VCM and then divide by the magnitude of the gain. For example, if the output voltage was 2.4V and VCM was 2.5V with a gain of 20 the offset would be (2.5V-2.4V)/20 = an offset of 5mV.


In the folllowing images, the measured VCM will be on the left and the measured Vout will be on the right.
     

LM324

(2.4959V - 2.4940v)/20 = 95uV

          

LM339

(2.4975V - 2.4922V)/20 = 265uV

     

LM348

(2.4999V - 2.5157V)/20 = -790uV



     
TL081

(2.3835V - 1.9123V)/20 = 23.6mV

















 













      

 

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