EE 420L
Analog Integrated Circuit Design Laboratory
Laboratory Report 4: Op-Amps II, Gain-Bandwidth Product and Slewing

AUTHOR: Bryan Kerstetter

EMAIL: kerstett@unlv.nevada.edu

JANUARY 30, 2019

General Overview

This laboratory further introduces students to operational amplifiers. While also introducing concepts regarding the gain-bandwidth product and slewing. The gain-bandwidth product will then be used to calculate the bandwidths of op amp topologies with varying gains. Additionally, the slew rate of the LM324 Op Amp will also be calculated.

Prelab

I watched Dr. Baker’s second video about Op Amps while also reviewing the concepts covered in my Laboratory Report 3.

Description of Laboratory Procedures

{The LM324 is exclusively used throughout this laboratory}

{During this laboratory we assume that VCC+ = +5V and VCC- = 0V.}

{For oscilloscope images, assume that the yellow and blue traces are the input and output signals, respectively}

The Gain-Bandwidth Product

According to the LM324 datasheet, the gain-bandwidth product is 1.3 MHz as seen in Figure 1.

Figure 1

This gain-bandwidth product can be used to determine the open loop frequency response of the op amp as seen in Figure 2.

Figure 2

Bandwidths of a Non-Inverting Op-Amp Topology Under Various Gains

Hand Calculations

The bandwidth of a non-inverting op-amp topology with a certain gain can be calculated in the following manner.

[1]

Therefore, the bandwidths of a noninverting topology under various gains can be calculated.

[2]

[3]

[4]

Upon looking at Equations 2-3, we see that they are in agreement with the bode plot as seen in Figure 2. The gain of the non-inverting op-amp topology that we used can be seen in Equation 5.

[5]

Non-Inverting Topology: Gain of 1

We implemented the circuit as seen in Figure 3 on the breadboard. According to LTspice the bandwidth of simple LM324 voltage follower is 1.17 MHz as seen in Figure 4.

Figure 3

Figure 4

Experimentally, we were looking for when the output waveform is –3dB the magnitude of the input waveform. In other words, we were looking for what frequency the output waveform of 70.1 mVpp.

[5]

Figures 5 demonstrate the experimental results. The experimental results show that the bandwidth of 1.34 MHz

TEK00002

Figure 5

Non-Inverting Topology: Gain of 5

We implemented the circuit as seen in Figure 6 on the breadboard. According to LTspice the bandwidth 206 kHz as seen in Figure 7.

Figure 6

Figure 7

Experimentally, we were looking for when the output waveform is –3dB the magnitude of the input waveform. In other words, we were looking for what frequency the output waveform of 70.1 mVpp.

[6]

[7]

Figures 5 demonstrate the experimental results. The experimental results show that the bandwidth of 137.2 kHz

TEK00003

Figure 8

Non-Inverting Topology: Gain of 10

We implemented the circuit as seen in Figure 9 on the breadboard. According to LTspice the bandwidth 85.5 kHz as seen in Figure 10.

Figure 9

Figure 10

Experimentally, we were looking for when the output waveform is –3dB the magnitude of the input waveform. In other words, we were looking for what frequency the output waveform of 140 mVpp.

p [8]

[9]

Figures 11 demonstrate the experimental results. The experimental results show that the bandwidth of 83.15 kHz.

TEK00004

Figure 11

Comparing Hand Calculations, LTspice, and Experimental Results

Gain	Hand Calculations	Ltspice	Experimental Results
1	1.3 MHz	1.17 Mhz	1.34 MHz
5	260 kHz	206 kHz	137.2 kHz
10	130 kHz	85.5 kHz	83.15 kHz

Bandwidths of an Inverting Op-Amp Topology Under Various Gains

Hand Calculations

Figure 12

Figure 12 shows the circuit used to experimentally measure the bandwidth of inverting op-amp topology under different gains. The band width of a

[10]

[11]

Therefore, the bandwidths of a noninverting topology under various gains can be calculated.

[12]

[13]

[14]

Inverting Topology: Gain of -1

We implemented the circuit as seen in Figure 13 on the breadboard. According to LTspice the bandwidth 688 kHz as seen in Figure 14.

Figure 13

Figure 14

Experimentally, we were looking for when the output waveform is –3dB the magnitude of the input waveform. In other words, we were looking for what frequency the output waveform of 70.1 mVpp.

[15]

Figures 15 demonstrate the experimental results. The experimental results show that the bandwidth of 5.75 MHz This frequency is vastly different when compared to our theoretical and experimental values. This reason for this is unknown. Possibly, there were some factors that we did not take in account.

Figure 15

Inverting Topology: Gain of -5

We implemented the circuit as seen in Figure 16 on the breadboard. According to LTspice the bandwidth 149 kHz as seen in Figure 17.

Figure 16

Figure 17

Experimentally, we were looking for when the output waveform is –3dB the magnitude of the input waveform. In other words, we were looking for what frequency the output waveform of 70.1 mVpp.

[16]

[17]

Figures 18 demonstrate the experimental results. The experimental results show that the bandwidth of 225 kHz The oscilloscope was not properly reading the frequency. Therefore, the reading of 225 kHz comes from the function generator.

Figure 18

Inverting Topology: Gain of -10

We implemented the circuit as seen in Figure 19 on the breadboard. According to LTspice the bandwidth 78.4 kHz as seen in Figure 20.

Figure 19

Figure 20

Experimentally, we were looking for when the output waveform is –3dB the magnitude of the input waveform. In other words, we were looking for what frequency the output waveform of 140 mVpp.

p [18]

[19]

Figures 11 demonstrate the experimental results. The experimental results show that the bandwidth of 108 kHz. The oscilloscope was not properly reading the frequency. Therefore, the reading of 108 kHz comes from the function generator.

Figure 21

Comparing Hand Calculations, LTspice, and Experimental Results

Gain	Hand Calculations	Ltspice	Experimental Results
-1	650 kHz	688 khz	5.75 MHz
-5	216 kHz	149 kHz	225 kHz
-10	118 kHz	78.4 kHz	108 kHz

The LM324 Slew Rate

An op-amp’s slew rate is the rate at which voltage change. In other words, slew rate Figure 22 depicts the circuit we designed to measure the slew rate of the LM324. The design implements a simple unity gain non-inverting topology. Vsignal is where the signal will be placed. In this laboratory, we built a circuit where Vsignal was a pulse and a square wave.

[20]

Figure 22

Slew Rate with Pulse Vsignal Input

In Figure 23 we see that the 5 kHz frequency is not great enough for the LM324 slew rate to be a huge factor. However, at the greater frequency of 170 kHz we can evidently see the effect of the slew rate (Figure 24). The slew rate can be calculated based upon the cursor measurements seen in Figure 24.

[21]

Figure 23: 5 kHz

Figure 24: 170 kHz

Slew Rate with Sinusoid Vsignal Input

In Figure 25 we see that the 10 kHz frequency is not great enough for the LM324 slew rate to be a huge factor. However, at the greater frequency of 170 kHz we can evidently see the effect of the slew rate (Figure 26). The slew rate can be calculated based upon the cursor measurements seen in Figure 26.

[22]

Figure 25: 10 kHz

Figure 26: 170 kHz

Slew Rate According to the LM324 Datasheet

The slew rate per the LM324 data sheet is 400 mV/µs when the given parameters are implemented.

Figure 27

Comparing Slew Rate Values

	Sinusoid Vsignal	Pulse Vsignal	Datasheet
Slew Rate (mV/µs)			400

There is little difference between our experimental slew rates under pulse and sinusoid Vsignals. However, there was a much more significant difference between the experimental slew rates and the slew rate given in the LM324 datasheet. This difference is most likely due to the fact that our slew rate test circuit was most likely different than STs slew rate test circuit. Additionally, the slew rate in the datasheet was given with a whole host of parameters as seen in Figure 27. Our test circuit parameters were much different.

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