by Prof. Thomas Zimmer and Prof.
Didier Geoffroy
University Bordeaux 1, France
copyright, last modified: March 2004
A two stage feedback amplifier will be studied. Its open-loop characteristics will be compared to its closed loop behaviour.
Feedback
Series shunt feedback
Gain sensitivity
Non-linear distortion
Bandwidth enlargement
Input and output impedance modification
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:
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.
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.:
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.
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.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.
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:
Attention: keep VOSC under 15mV and the maximum frequency below 100kHz !!!
Figure 7: Measurement set-up for amplifier output impedance determination
The value of the load RL is: | 10 kΩ |
Attention: keep VOSC under 25mV and the maximum frequency below 100kHz !!!
From the measured curve and the previous result determine the output impedance.
Give the analytical expression for the output impedance. Write
your results here
Figure 8: Configuration for the input impedance determination
The value of R0 is: | 1 kΩ |
Attention: keep VOSC under 30mV and the maximum frequency below 100kHz !!!
From the measured curve and the previous result determine the input impedance.
Give also the analytical expression for the input impedance. Write
your results here
Figure 9: Top level schematic of the two-stage voltage amplifier in closed loop
configuration
Attention: keep VOSC under 50mV and the maximum frequency below 100kHz !!!
Figure 10: Measurement set-up for amplifier output impedance determination
The value of the load RL is: | 2 kΩ |
Attention: keep VOSC under 100mV and the maximum frequency below 100kHz !!!
From the measured curve and the previous result determine the output impedance.
Figure 11: Measurement set-up for amplifier input impedance determination
The value of R0 is: | 4,7 kΩ |
Attention: keep VOSC under 100mV and the maximum frequency below 100kHz !!!
From the measured curve and the previous result determine the input impedance.
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 |
Attention: keep VOSC under 15mV and the maximum frequency below 100kHz !!!
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 |
Attention: keep VOSC under 30mV and the maximum frequency below 100kHz !!!
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
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):
We are using now the configuration of figure 4, where, again, the distortion elements of
Measurement in the time domain (info):