Lab Experiment: Feedback amplifier

by Prof. Thomas Zimmer and Prof. Didier Geoffroy
University Bordeaux 1, France
copyright, last modified: March 2004

Contents


Aim of the lab exercise

The described lab exercise takes place in the curriculum of electrical engineers. The topic is analogue electronics. The objective of the lab is to familiarise the students with the concept of feedback. The influence of feedback with respect to gain, bandwidth, input and output impedance, sensitivity and non-linear distortion is investigated.

A two stage feedback amplifier will be studied. Its open-loop characteristics will be compared to its closed loop behaviour.

 

Keywords

Feedback
Series shunt feedback
Gain sensitivity
Non-linear distortion
Bandwidth enlargement
Input and output impedance modification


1 Prelab

1.1 Principle of negative feedback

The principle of a feedback amplifier can be studied as follows. Consider the feedback configuration of figure 1:


Figure 1: Principle of feedback configuration

 

The basic amplifier is in principle not ideal: It has a not infinite input impedance, its output impedance is not zero. Under these conditions the feedback network will influence the open loop gain, where its output and input impedance will load the input and output impedance of the basic amplifier, respectively.

Some definitions:

1.2 Series shunt feedback

There are four basic feedback amplifier connections. These are specified according to whether the feedback signal is voltage or current and the output signal which is sampled is a voltage or current. So we have: Series shunt feedback, Shunt shunt feedback, Shunt series feedback, Series series feedback.

In this lab exercise the Series shunt feedback configuration will be investigated. In this configurations all signals (, , ...) are voltages, and all the gains (, , ) are voltage gains (c.f. figure 2)


Figure 2: Series shunt feedback configuration

 

Investigation of the open loop amplifier can be done by modifying the previous schematic (figure 2) in the following manner (figure 3). The influence of loading effects of the feedback network is taken into account:


Figure 3: Feedback loaded open loop of the Series shunt feedback configuration

The amplifier gain in the closed loop is related to the open loop gain by the following relation ship:

(1)

For this type of feedback configuration, the input impedance and the output impedance of the closed loop amplifier can be calculated from the input impedance and the output impedance of the open loop amplifier using the following relationships:

(2), and (3)

The Series shunt feedback increases the input impedance and decreases the output impedance. This is very often wanted, so this type of feedback is of particular interest.

1.3 Some feedback properties

Besides the already mentioned change of the output and input impedance, a feedback improves some a the key figures of merit of an amplifier, whatever the feedback configuration is, e.g.:

1.4 Theoretical study

We will apply the series shunt feedback to the following two stage voltage amplifier (figure 4).


Figure 4: Two stage voltage amplifier with Series shunt feedback configuration

The value of the components are (table 1):

C1 = 330nF   R1 = 1 kΩ   R2 = 82 kΩ
R3 = 22 kΩ R4 = 22 kΩ R7 = 10 kΩ
R5 = 47 kΩ R6 = 1,8 kΩ opamp LT 1490

 


Figure 5: Feedback loaded open loop representation of the 2-stage voltage amplifier

Using this representation we will determine the characteristics of the open loop amplifier and in a final step recalculate the properties of the closed loop amplifier.

In the first part we have shown, that the feedback amplifier characteristics can be calculated from the open loop configuration (1), (2) and (3). This is in general done in this way, because the calculations in the open loop configuration are much easier and can often be performed without a simulation tool. We will do these calculations for our 2-stage amplifier in two steps. First in a very simplified approach, secondly in a more realistic approach.

A - We assume in a first approach the amplifiers as ideal (input impedance is infinite, output impedance is zero and differential gain is infinite).

B - Now, we assume, that our basic amplifier is characterised by a first order response behaviour (single pole): (, -3dB frequency @ , and gain bandwidth product = 200kHz, the input and output impedances are still ideal).

Calculation of the open loop gain :

This calculation can be performed, in a first approach, by calculating three different transfer functions: one for the opamp 1: , one for the opamp 2: , and one for the voltage divider at the output .

 

Straight forward investigation of :

The transfer function can be rewritten in the following way :

with and

From the former expression of a more convenient form of can be found:

with and

Remark: these expressions are not exact, they represent a good approach, when appropriate numerical values for the components are used.

From the previous results we can determine now the characteristics of the feedback amplifier.


2 Simulation

On-line electrical simulation tools are available at:

You can also free download SPICE type circuit simulators (evaluation version) at: Use one of these tools to simulated the circuits discussed above. Compare it to the theoretical results.

3 Experiments

The subject of this lab exercise consists in investigating the influence of feedback to the main characteristics of an amplifier. In a first step the open loop architecture is investigated. The transfer characteristic, input and output impedance are determined. Next, the loop is closed and the measurements are repeated. The results are compared to the theoretical and simulation results. Further, the sensitivity of the open loop and the closed loop configuration with respect to a change of device parameter values are investigated. Finally, a non-linear distortion is introduced in the amplifier. It can be observed that this distortion is reduced in the case of the feedback configuration.

3.1 Open loop configuration

3.1.1 Amplifier gain (open loop)

The hardware implementation is shown on figure 5 for the two-stage voltage amplifier in open loop configuration. For further investigation, it will be represented as shown on figure 6:


Figure 6: Top level schematic of the feedback loaded two-stage voltage amplifier in open loop configuration

 

The value of the components are listed in table 1:

Measurement in the frequency domain (info),

hp4194a Perform a measurement.

Attention: keep VOSC under 15mV and the maximum frequency below 100kHz !!!

 

3.1.2 The output impedance (open loop)

The output impedance of the open loop configuration can be determined by measuring the voltage gain without load (previous result) and with a known load (next measurement). The hardware implementation is shown on figure 7.


Figure 7: Measurement set-up for amplifier output impedance determination

 

The value of the load RL is: 10 kΩ
Measurement in the frequency domain (info),

hp4194a Perform a measurement.

Attention: keep VOSC under 25mV and the maximum frequency below 100kHz !!!

3.1.3 The input impedance (open loop)

The input impedance of the open loop configuration can be determined by connecting a known load in series between the circuit under test and the signal generator. From the voltage gain without series resistance, the voltage gain with series resistance (next measurement) and the known series resistance value the input impedance can be deduced. A symbolic schematic is shown on figure 8.

 


Figure 8: Configuration for the input impedance determination

 

The value of R0 is: 1 kΩ
Measurement in the frequency domain (info),

hp4194a Perform a measurement.

Attention: keep VOSC under 30mV and the maximum frequency below 100kHz !!!

 

3.2 Closed loop configuration

3.2.1 Amplifier gain (closed loop)

The hardware implementation is shown on figure 4 for the two-stage voltage amplifier in closed loop configuration, a simplified schematic is shown on figure 9.


Figure 9: Top level schematic of the two-stage voltage amplifier in closed loop configuration

Measurement in the frequency domain (info),

hp4194a Perform a measurement.

Attention: keep VOSC under 50mV and the maximum frequency below 100kHz !!!

 

3.2.2 The output impedance (closed loop)

The output impedance is determined in the same manner as before (c.f. 3.1.2). The hardware implementation is shown on figure 10 of the loaded 2-stage voltage amplifier in closed loop configuration.


Figure 10: Measurement set-up for amplifier output impedance determination

 

The value of the load RL is: 2 kΩ
Measurement in the frequency domain (info),

hp4194a Perform a measurement.

Attention: keep VOSC under 100mV and the maximum frequency below 100kHz !!!

 

3.2.3 The input impedance (closed loop)

The input impedance is determined in the same manner as before (c.f. 3.1.3). A simplified representation is shown on figure 11.


Figure 11: Measurement set-up for amplifier input impedance determination

 

The value of R0 is: 4,7 kΩ
Measurement in the frequency domain (info),

hp4194a Perform a measurement.

Attention: keep VOSC under 100mV and the maximum frequency below 100kHz !!!

 

3.3 Sensitivity investigation

3.3.1 Transfer characteristic (open loop)

Now we investigate the sensitivity of the open loop configuration with respect to the closed loop configuration. One of the circuit parameter values has been changed for both configurations. For the open loop configuration the hardware implementation is the same as shown on figure 5.

The value of the changed component R2 is 68 kΩ
Measurement in the frequency domain (info),

hp4194a Perform a measurement.

Attention: keep VOSC under 15mV and the maximum frequency below 100kHz !!!

 

3.3.2 Transfer characteristic (closed loop)

For the closed loop configuration the hardware implementation is the same as shown on figure 4.

The value of the changed components are the same as before: R2 = 68 kΩ
Measurement in the frequency domain (info),

hp4194a Perform a measurement.

Attention: keep VOSC under 30mV and the maximum frequency below 100kHz !!!

 

3.4 Non linear distortion

First, we introduce a non linear element in the 2-stage amplifier. This is done by modifying the feedback loop of A2 as shown on figure 12. To understand this non linearity, let us consider the diodes like switches. If the voltage drop through the diodes is smaller than 0.7V, they act like an open circuit. In this case A2 in an inverter with a voltage gain of -(47+22)/22=-3.1 (R8=47 kΩ R4=22 kΩ R3=22 kΩ). When the voltage drop is higher than 0.7V, they act like a short circuit. Now the inverter gain is equal to -1. That means that this amplifier has two different states. The corresponding output signal cannot be related by a linear relationship to its input signal. In fact, it depends on the input signal level.


Figure 12: Non linear element introduced in A2 to generate distortion

3.4.1 Non linear distortion in open loop configuration

We are using the configuration of figure 5, where the distortion element of figure 12 has been added. The measurements are done in the time domain. (Signal generator and oscilloscope). Working inside the bandwidth, determine a appropriate measurement frequency and calculate the input signal level, to have an output signal amplitude of 3V peak-to-peak.

Measurement in the time domain (info):

scope Perform a measurement.

3.4.2 Non linear distortion in closed loop configuration

We are using now the configuration of figure 4, where, again, the distortion elements of

Measurement in the time domain (info):

scope Perform a measurement.

4 Discussion