13B: Gain-Bandwidth product

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13B: Gain-Bandwidth product#

Learning goal: understand how properties of an op-amp like GB product and slew rate might affect the measurements. Make a circuit to experimentally observe them. Structure of an experiment:

Background + Predict + Stimulate (40 min): This is homework and should be finished before you start your 4 hours practicum session. (To be done individually)
Build + Measure (55 min): with your partner (group of 2)
Evaluate (10 min): with a group of 4 (per table)

BACKGROUND Gain-Bandwidth product and slew rate of OPAMPs#

⏳ Estimated time: 10 min

non-ideal OPAMP#

An ideal OPAMP would have an infinite gain, based on the feedback theory, this would give us ideal amplifiers with infinite bandwidth. In real life the gain of an OPAMP is extremely high (>100dB), but not infinite, and even worse it drops with increasing frequency.

The gain at DC is referred to as \(A_o\). This very high gain is valid from DC to a specific frequency of the amplifier, the bandwidth. After this “bandwidth-frequency” the gain of the amplifier starts to drop with 20dB/decade, similar to a first order low-pass filter (e.g. like a RC-filter). The gain will continue to drop, at a certain moment the gain of the OPAMP itself will be equal to 1x (0dB), this frequency is called the unity-gain frequency. The product of the bandwidth-frequency and Ao gives us a number. This number is expressed in “Hz”. The frequency we get from this multiplication corresponds to the unity-gain frequency. When further investigating on this, one could find that the product of the gain and the bandwidth of the amplifier is a constant. This constant is referred to as the Gain-Bandwidth product, or GB-product in short. In this experiment we will “prove” that the product of the gain and the bandwidth is a constant.

\[ \mathrm{gain} \cdot \mathrm{bandwidth} = \mathrm{constant} = \mathrm{GB} \]

bandwidth of active networks#

Up till now we were used to measure the bandwidth of passive networks. As a result of this the maximum gain was always 1x (0 dB). The cut-off frequency was always found at the -3dB point, which corresponded to a transfer of 0.71x (square root of 0.5).

Now we are looking at the bandwidth of amplifiers with a gain (usually) bigger then 1x (0 dB). The voltage gain of such an amplifier could be e.g. 10x which equals 20 dB. The bandwidth of such an amplifier is specified as the frequency where the gain of the amplifier has dropped by -3 dB.

The resulting gain of the amplifier is then 20 dB – 3 dB = 17 dB, which corresponds to a factor of 7.1x. So, in order to determine the bandwidth of such an amplifier, we need to find the point where the gain is 7.1x instead of 0.71x. Another example, when the gain is 26 dB, thus 20x, we need to find the point where the gain is 26 dB – 3 dB = 23 dB, thus 14.1x.

slew rate#

Another parameter which will influence the performance of our amplifier is the slew-rate. The slew-rate of an amplifier can influence the performance of an amplifier such that it looks like a bandwidth limitation, however the underlying principle is different. Slew rate has to do with limitation in speed at which the output voltage of the OPAMP can change. Thus the slew-rate indicates the voltage change of the output per unit of time, in general it is expressed in Volts per microsecond (V/us). This maximum speed of change is a characteristic of the OPAMP and it is constant (does not depend on frequency!).

The effect of the slew-rate is indicated in the picture below. The input signal (Ui) here is a square wave, the output signal shown is supposed to be a square wave as well. However, due to the finite speed at which the output can change it will be a trapezium-shaped waveform at medium frequencies and becomes a triangle at high frequencies.

A common mistake is that people only look at the peak-to-peak values of a signal when measuring the gain. They neglect the distorted waveform, this will lead to a confusion between gain limitation due to the bandwidth or due to the slew rate.

When repeating the measurement with lower amplitude signals gives you different results for the bandwidth, it might be that you are “fooled” by the slew rate . A final note on slew rate, some OPAMPs have an extremely high slew rate (e.g. 100V/us), others have a fairly low slew rate (e.g. 0.5V/us). So where slew rate can be a limiting factor with one type of OPAMP, and is of no limitation with another OPAMP.

ANTICIPATE: signals used to experimentally measure bandwidth and slew#

⏳ Estimated time: 15 min

Using certain input signals you can easly observe bandwidth and slew rate on the output.

Explain how to measure the bandwidth experimentally. Include which input signal to use and how to interpret the results.
Explain how to measure the slew rate. Again, include which input signal to use and how to interpret the results.

### TO DO="your proposed measurement for bandwidth and slew rate"

SIMULATE:#

⏳ Estimated time: 15 min

Download the circuit named ‘week13B’ from Brightspace from LTSpice resources. Pick the correct simulation settings yourself!!

Determine the gain-bandwidth product.

### TO DO="your found gain-bandwidth product"

ℹ️ Hint

Make sure the circuit is built correctly

Check whether you are measuring at the correct spots.

Precap to be updated: https://www.youtube.com/watch?v=MSqN1yLn9ko

IMPLEMENT & INVESTIGATE 1: Gain-Bandwidth product calculations#

⏳ Estimated time: 30 min

You will need:

testboard 4
oscilloscope
function generator
all necessary cables
testboard 4 scheme (to know where different resistors are located) - you can find this on Brightspace: Resources > Studio Classroom Resources > Test Boards

Build the circuit given below and connect the function generator to the input. Use 1Vpp amplitude (to avoid already looking at the slew rate). Connect the oscilloscope to display both the input signal and the output-signal of the amplifier.

By now you know the drill: verify your predictions with the circuit above. There is a table below that you can use.

Ra	Rb	Gain (calculated)	Bandwidth (measured)	GB-product
1kOhm	1kOhm	?	?	?
1kOhm	10kOhm	?	?	?
1kOhm	100kOhm	?	?	?
1kOhm	1MegOhm	?	?	?

Do you notice any patterns?
Is it what you expected?

### TO DO="conclusion based on the data on the GB product"

ℹ️ Hints

Remember that the bandwidth is the frequency at which the gain drops with 3 dB
Make sure the output signal does not clip. The easiest way to do so is to reduce the Vpp of the input signal.
You can use the absolute gain, \(|\mathrm{gain}|\), here.

IMPLEMENT & INVESTIGATE 2: observe slew rate#

⏳ Estimated time: 20 min

Using the same LM741 op-amp, choose the proper resistors for a gain of 20 dB (gain=-10). Connect the function generator to the amplifier input and the output to the oscilloscope. Set the generator for a 1 Vpp square wave with, frequency 1 kHz and a duty-cycle of 50%.

The slew rate will be visible as a steadily rising or falling output signal, while the input is a square wave with sharp edges.

Determine the slope of the rising and falling edge.

optional challenge: 20 min
the slew rate limits the ‘bandwidth’. Increase the frequency of the generator, and observe how (and at which frequency) the slew rate limits the bandwidth.

### TO DO="your value for the slew rate"

IMPLEMENT & INVESTIGATE 3: validate your results#

⏳ Estimated time: 5 min

Reflect whether your measurement value for the GB-product is in agreement with the value in the data sheet of the LM741 (https://www.ti.com/product/LM741, look for bandwidth/GBW). If not, what might be the cause?
Is your measurement for the slew rate is in agreement with the value in the datasheet. If not, what might be the cause?

### TO DO= comparison measurements with GB spec

COMPARE & CONCLUDE#