Lab 4 – Op-Amps II: Gain-Bandwidth Product & Slewing

EE 420L Analog IC Design

Lab Date: 2/20/19 Due: 2/27/19

By David Santiago – Email: santid4@unlv.nevada.edu

Last Edited on 2/20/19 at 9:58pm using Word

  

Lab description:

Suppose we have an Operational Amplifier (Op-Amp) and we would like to operate the Op-Amp at different frequencies. Ideally, we can tell ourselves that we can get any Gain at any frequency that we want, however, the world is not perfect and there will be some drawbacks for wanting to have high-speed circuits. All of these gains will all “roll-off” and unify at one given point at dB = 0 (gain of 1), and this point is called the Unity Gain Frequency. The roll-off point for higher gains is called the Bandwidth.

-Also, suppose we want to send some very fast pulse through an amplifier. We will also realize that there are device limits set so that we can have a certain volt gain per certain time. This certain parameter on the device that will give us this limit is called the Slew Rate.

 

In this lab, we will be figuring out the bandwidth frequency (or f3DB or roll-off frequency) for both the Non-inverting and Inverting Op-Amp topology. Also, we will build a simple circuit so that we can find the point where the Op-Amp’s output will show its slew rate for both a square wave and a sine wave.

 

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Experiment 1: Non-inverting Op-Amp

 

 In this experiment, we will build the non-inverting op-amp and testing out gains of 1, 5, and 10 and finding the Bandwidth frequencies of these gains, respectively.

 

Before we do these experiments, we will need to prove these bandwidth frequencies using 2 methods:

Method A. Hand Calcs:

To solve for this bandwidth frequency, we will need a simple equation to solve for our frequencies.

The Gain-Bandwidth equation will be given by:

                              

                               Gain * Bandwidth = Open Loop Gain (constant)

 

 

From the datasheet, the Wide Gain Bandwidth for the LM324 is: 1.3MHz

 

So, given a gain of 1 V/V and knowing the Bandwidth, We can say that:

               | 1 V/V | * 1.3MHz = 1.3M Open loop gain.

 

Theoretically, our bandwidth for a gain of 1 should be 1.3MHz.

 

For a gain of 5 V/V:     AoL / Gain     =Bandwidth

                                   = 1.3M / 5                 = 260kHz     

 

For a gain of 10 V/V:   1.3M / 10               = 130kHz

 

 

Method B. Looking at the Open Loop Gain Graph:

Suppose we are here to look for quick numbers and do not have access to our calculators. The datasheet will provide us with a graph and we can use this graph to estimate what our bandwidth will be for any given closed loop gain.

 

Here is a graph giving us our Open Loop Frequency Response, found in the LM324.pdf datasheet:

 

                              

 

 

So using our eyes, we can see that:

For a gain of 1:                                                           For a gain of 5:

          

      Bandwidth = 1.3MHz                  Bandwidth = ~300kHz

 

 

 

 

For a gain of 10:

                              

                          Bandwidth = ~150kHz

 

Here is a table recapping all of the hand-calculated Gains

Gain

1 V/V

5 V/V

10 V/V

Bandwidth

1.3MHz

260kHz

130kHz

 

 

Experiments:

For a gain of 1, we will be building what is called a Unity-Gain Amplifier, which is the Non-Inverting Op-amp topology but the output is fed back into the inverting terminal of the op-amp.

On the breadboard:

                                             

 

LTSpice Schematic:

              

 

The op-amp’s VCC+ and VCC- are 5V to 0V, respectively. The input will be a 1Vpp, 2.5V DC offset.

 

To find this bandwidth frequency, we will be looking for when our output is 70.7% of the input.

NOTE: .707 comes from doing 1 / sqrt(2), where both our real and imaginary parts are equal to 1.

 

 

Bandwidth for Gain of 1:

Here we can see that we will get this bandwidth frequency at:

Bandwidth = around 1.3MHz

 

To simulate this Roll-off in LTSpice, we will do a simple calculation:

 

Since we will want a Low-pass bandwidth, we will do this circuit inside our Op-amp circuit:

 

                      

 

For the capacitor, we will use the RC time constant. From the datasheet, at a low frequency of 10Hz, and given a resistance of 1 ohm, f3dB = 1 / (2πRC) => Capacitor = 1 / (2π(1)(10Hz)) = 0.0159 Farads

 

Here is our LTSpice Gain of 1 output:

 

As you can see, the 3dB value will be at around 1MHz. The reason for this inaccuracy is that we have created our own ideal Op-Amp, but we want to estimate and try to simulate what it will look like on the board.

 

Gain of 5:

For a gain of 5, we will be using RF = 4kΩ and RI = 1kΩ so that our Non-Inverting gain will be:

ACL = | 1 + (4/1) | = 5 V/V

On The breadboard:

              

NOTE: RI’s Terminals are connected to a 2.5V DC battery source and to the Inverting Terminal.

 

LTSpice:

                      

 

Output:

                      

NOTE: 100mVpp*5/2 *(.707)= 176mV

The point that we get to see that the Output rolls off to 70.7% of the input is at

Bandwidth = 190kHz

 

LTSpice Output:

 

 

From here, we have our top dB of 14dB and subtracted 3dB to get 11dB. F = 202KHz

 

Gain of 10:

We will swap out RF = 9k and RI = 1k so that we will get a gain of 10.

 

LTSpice:

                      

 

Output:

                      

NOTE: 100mV*10/2 * (.707) = 352mV

Bandwidth = 96kHz

 

LTSpice Output:

20dB – 3dB = 17dB, Bandwidth = 100kHz.

 

Gain

1 V/V

5 V/V

10 V/V

Experimental

~1.3MHz

190kHz

96kHz

Hand Calc

1.3MHz

260kHz

130kHz

LTSpice (Ideal)

1MHz

202kHz

100kHz

 

From the table, we can conclude that our hand calcs are in the ballpark on where our experimental bandwidths are. For LTSpice, it was used as a reference to estimate where the roll-off frequency is.

 

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Experiment 2: Inverting Op-Amp

 

For this experiment, we will do what we did in experiment 1 but for the inverting op-amp topology.

 

For this, we will use our simple equation:

 

                               Gain * Bandwidth = Open Loop Gain (constant)

 

HOWEVER, The actual equation we will use is:

 

    | 1 + Rf/Ri | * Bandwidth = AoL

 

Then to find the Gain-Bandwidth Product:

    | Inverting gain | * BW = Gain-Bandwidth Product.

 

 

Gain of 1:

Bandwidth = 1.3M / [ 1 + (10k/10k) ] = 650kHz

And our Gain-Bandwidth Product is:

        | -10k/10k | * 650kHz = 650k

 

Gain of 5:

Bandwidth = 1.3M / [ 1 + (50k/10k) ] = 217kHz

GBP = |-5 | * 217kHz = 1.08M

 

Gain of 10:

Bandwidth = 1.3M / [ 1 + (100k/10k) ] = 118kHz

GBP = |-10| * 118kHz = 1.18MHz

 

Table of Hand Calculated Gains:

Gain

-1 V/V

-5 V/V

-10 V/V

Bandwidth

650kHz

217kHz

118kHz

GBP

650K

1.08M

1.18M

 

Experiments:

Gain of -1:

Our Rf = 10k and Ri = 10k

On the breadboard:

                      

 

LTSpice:

       

 

Output:

              

Bandwidth = 800kHz

 

LTSpice Output:

 

Bandwidth = 502kHz

 

 

Gain of -5:

We replaced the Rf with 50k and kept Ri = 10k

 

LTSpice:

              

 

Output:

              

Bandwidth = 150kHz

 

LTSpice Output:

Bandwidth = 166kHz

 

 

Gain of -10:

We replaced Rf with 100k and kept Ri = 1k

 

LTSpice:

              

 

Output:

              

Bandwidth = 83kHz

 

LTSpice Output:

Bandwidth = 90kHz

 

Gain

-1 V/V

-5 V/V

-10 V/V

Experimental

800kHz

150kHz

83kHz

Hand Calc

650kHz

217kHz

118kHz

LTSpice (Ideal)

502kHz

166kHz

90kHz

 

Fromm the table, we are a bit off when we are dealing with lower gains, but as the gains increase, our Experimental and hand calcs get closer to each other. On the other hand, we can see that the ideal LTSpice simulation is also getting close to our experimental results as we increase the gain.

 

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Experiment 3: The Slew Rate

In this experiment, we will be building 2 simple circuits, a unity follower circuit with a square input, and a unity follower circuit with a sine input. For that we will do the following circuit:

 

                              

NOTE: This is the non-inverting topology with an AC input at 2.5V DC offset.

 

We will be sending a Square wave through the Op-Amp so that we can visually see the slew rate of the Op-Amp.

 

For that, we decided to stop increasing the frequency until we start seeing a “triangle” wave.

 

Output:

              

From the cursors that we placed onto the blue output, we can use our old formula friend:

 

               Slew Rate = Rise (Voltage difference) / Run (Time difference)

 

From the cursors (and measured difference using the Oscilloscope):

        1.01V Voltage difference / 3.36us Time difference

          = 301 mV/us = .3 V/us

 

In the next circuit, we will be changing the input from a square wave into a sine wave:

For the sine wave, we can mathematically hand calculate this. Taking a derivative of the sine wave, we will be left with:

 

             2πf*Vin ≤ Slew Rate

 

So, given an input of 1V, and from the datasheet, we have a Slew Rate of .4 V/us

 

Knowing this, we can solve for frequency:

        F ≤ SR / (2πVin) = (.4/10^-6) / (2π) = 63.6 kHz

 

Output:

              

 

From cursors:

1.05V Change / 3.6us Change = 292 mV/us = .292 V/us

 

From looking at both the slew rates of the Square wave and the sine wave, we can conclude that the slew rate for this Op-Amp is 300 mV/us = .3 V/us

 

Input

Slew Rate

Square Wave

.301 V/us

Sine wave

.292 V/us

Datasheet

.4 V/us

 

From the table, we can conclude that our experimental slew rate is close enough to our datasheet slew rate.

Since this is a parameter that is built-in to the Op-amp, the parameter is experimental throughout many other Op-amps, just like from Lab 3, where our Voffset voltage was different between different Op-amps.

 

 

 

 

 

 

 

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