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=====Op-Amp Output Stages - ADALM1000=====
==== Introduction ====
Negative feedback shows up throughout all of the natural world, and thus existed long before it was discovered and used by engineers to design useful products.  The way the iris diaphragm controls the amount of light that enters the eye provides a good example of negative feedback from the natural world.  When the light entering the eye exceeds the optimal level, the iris closes until the light level is reduced to the optimal level.  Similarly, when the light entering the eye is below the optimal level, the iris opens until the light level is raised to the optimal level.  Clearly, there are limits to the operation of this natural negative feedback system.  For instance, the optimal light level can never be reached no matter how wide the iris opens when the eye is in total darkness.  The important thing to note is that the operation of the negative feedback system is based on controlling something (the iris opening in this case) in such a way as to reduce the error between a desired condition and an existing condition.  The error is detected and the system adjusts itself in a direction that reduces the error.  When there was too much light entering the eye, the error was positive seeing that the difference between the light entering the eye and the optimal light level was positive, and negative feedback operated on the system in such a way as to move the system in a direction //opposite// to that of the error.  This action involved reducing the diameter of the iris opening until the error between the actual light entering the eye and the optimal light level was reduced to its minimum.  In all realizable systems, the error can only be reduced to a minimal level, and cannot be reduced all the way to zero.

Another good example of a negative feedback system is how the speed of a car is controlled.  When a person is controlling the speed, the person observes the car's speedometer and adjusts the car's speed using the accelerator pedal or brake pedal in order to minimize the error between the actual speed and the desired speed.  When the actual speed is higher than the desired speed, the error is positive so the brake pedal is applied in order to move the speed in the opposite direction of the error -- or in a negative direction -- in order to reduce the error.  Similarly, when the actual speed is lower than the desired speed, the error is negative so the accelerator pedal is applied in order to move the speed in the opposite direction -- or in a positive direction -- in order to reduce the error.  In both cases, the speed of the car is moved in a direction which is the //negative// of that of the error, and this is the origin of the term //negative feedback//.  The previous example is an example of a negative feedback system in which a person is part of the feedback loop.  Automatic cruise control systems use electromechanical means in place of the person to implement the negative feedback.

==== Objective ====

To study and understand push-pull Class B amplifiers constructed with BJTs as the amplifying elements and view the characteristic crossover distortion associated with them.  To see how using level shifters to add a small amount of bias to the Class B amplifier sections to produce a push-pull Class AB amplifier can significantly reduce crossover distortion.  To understand how the crossover distortion mechanism differs from other distortion mechanisms, and gets worse as a percentage of signal amplitude as the output signal gets smaller.  To understand how thermal runaway can occur in Class AB amplifiers and investigate techniques to prevent it.  Following completion of this lab you should be able to explain the basic operation of push-pull Class B and Class AB amplifiers that use BJTs as the amplifying elements, describe crossover distortion, explain how and why it happens, and how it differs from distortion caused by other mechanisms, describe what level shifters do, and explain what can cause thermal runaway in Class AB amplifiers, why it can be dangerous, and how it can be prevented.
==== Materials and Apparatus ====
  * Data sheet handout for the 2N3904 NPN transistor
  * Data sheet handout for the 2N3906 PNP transistor
  * Analog Devices ADALM1000 (M1K)
  * Solderless breadboard and jumper wires from the ADALP2000 Analog Parts Kit
  * (2) 2N3904 NPN transistor from the ADALP2000 Analog Parts Kit
  * (2) 2N3906 PNP transistor from the ADALP2000 Analog Parts Kit
  * (4) 1.1 Ω resistor from the ADALP2000 Analog Parts Kit
  * (1) 100 Ω resistor from the ADALP2000 Analog Parts Kit
  * (2) 1.0 KΩ resistor from the ADALP2000 Analog Parts Kit
==== Procedure ====
  - Construct the following circuit on the solderless breadboard{{ university:courses:engineering_discovery:lab_14_image_1.png?800 }}
  - Refer to the illustration below for one way to install the components in the solderless breadboard{{ university:courses:engineering_discovery:lab_14_assembly_image_1.png?1000 }}
  - Plug in the M1K using the supplied USB cable and launch software
  - Set up the M1K to source voltage/measure current on Channel A and measure voltage on Channel B
  - Set up Channel A source waveform for a 50 Hz “Sine” output that swings between 0.5 V and of 4.5 V
  - Observe the output voltage at the connection between the two emitters on Channel B and observe the large amount of crossover distortion that is present in the output signal as shown in the image below{{ university:courses:engineering_discovery:lab_14_image_2.png?1000 }}
  - Construct the following circuit on the solderless breadboard{{ university:courses:engineering_discovery:lab_14_image_3.png?800 }}
  - Refer to the illustration below for one way to install the components in the solderless breadboard{{ university:courses:engineering_discovery:lab_14_assembly_image_2.png?1000 }}
  - Set up Channel A source waveform for a 50 Hz “Sine” output that swings between 1.0 V and of 4.0 V
  - Observe the output voltage at the connection between the two emitters on Channel B and observe how the crossover distortion has been significantly improved due to the addition of the level shifting transistors, connected as diodes
  - Estimate the voltage loss factor due to the voltage divider formed between the amplifier output resistance and the load resistance
  - Increase the input voltage amplitude to swing between 0.5 V and 4.5 V and observe the output waveform clipping that occurs due to the headroom loss incurred by the level shifters
==== Theory ====
In the lab we observed the serious crossover distortion in a BJT-based push-pull Class B amplifier that occurs due to the required ≈ 0.7 V V<sub>BE</sub> bias voltage.  The clear solution to this problem was to add just enough DC bias voltage such that each transistor is slightly conducting collector current with no signal applied to the amplifier input.  This solution works quite well, but has a few drawbacks, one of which is the potential for thermal runaway.

Thermal runaway is a form of positive feedback, sometimes referred to as a self-reinforcing feedback loop, in which a change in a system operating condition pushes the system away from a desired stable point instead of toward a stable point.  Stable systems are designed using //negative feedback// in which changes in the system operating conditions push the system back toward its desired stable state.  A simple example of a naturally-occurring negative feedback system is the system that regulates the amount of light that enters the eye by controlling the diameter of the iris diaphragm.  When the light entering the eye increases beyond the ideal amount, the iris diaphragm decreases in diameter until the light reaches its ideal level.  Similarly, when the light entering the eye decreases below the ideal level, the iris diaphragm increases until the light reaches its ideal level.  Thus, negative feedback drives the system to //decrease// the error between an ideal condition and the actual condition.  Positive feedback systems do just the opposite of negative feedback systems.  A simple example of thermal runaway is what can can occur in carbon composition resistors that have negative temperature coefficients (NTC), that is, the resistances of these resistors decrease with temperature.  As a NTC resistor heats up its resistance decreases, causing it to draw more current, which further decreases its resistance, causing it to draw even more current, and so on.  If not limited by something, this process can continue until the resistor overheats and destroys itself.

Thermal runaway in BJT-based push-pull Class AB amplifiers occurs due to the negative temperature of the base-emitter voltage V<sub>BE</sub>.  The V<sub>BE</sub> temperature coefficient is typically about -2 mV/°C.  The worst bias arrangements for Class AB amplifiers with respect to thermal runaway are those that use bias voltages that are relatively fixed over temperature.  A resistive voltage divider network provides bias voltages that are relatively fixed with temperature, and this is why they are not widely used as Class AB amplifier bias circuits.  The following schematic illustrates a simple resistive voltage divider bias circuit that could be used to bias a BJT-based Class AB amplifier.{{ university:courses:engineering_discovery:lab_14_image_4.png?200 }}

The resistor values would be chosen such that R<sub>B1</sub> = R<sub>B4</sub> and R<sub>B2</sub> = R<sub>B3</sub>.  A potentiometer could also be placed between the two bases with a slightly different arrangement to provide an adjustable bias.  In the schematic above the input signal would be applied between R<sub>B2</sub> and R<sub>B3</sub>.  When properly designed, the voltage between the two bases would be equal to 2V<sub>BE</sub>(on) where V<sub>BE</sub>(on) is defined as the base-emitter voltage at which each transistor begins to conduct.  The thermal runaway problem with fixed bias can now be addressed.  As the base-emitter junction temperature increases, due to self-heating as well as potential ambient temperature increase, the base-emitter voltage would decrease by -2 mV/°C if it were not fixed by the resistive bias network.  The collector current and base-emitter voltage have an exponential relationship, which must be obeyed.  Since the base-emitter voltages are not allowed to decrease due to the fixed bias voltages provided by the voltage divider, the collector current increases instead according to the exponential dependence of I<sub>C</sub> on V<sub>BE</sub>.  This arrangement presents an exponential dependence of collector current on temperature.  As the collector current increases the base-emitter junction temperature increases, further increasing the collector current.  Much as was the case in the carbon composition resistor, we have an unstable self-reinforcing feedback loop in the amplifier which produces thermal runaway, and will eventually destroy the transistors.  Fortunately, there are a number of better biasing schemes that can be used to avoid thermal runaway.  

If we replace R<sub>B2</sub> and R<sub>B3</sub> with forward biased diodes, or transistors configured as diodes, we can cancel out the effects of the negative V<sub>BE</sub> temperature to a great degree as long as the current vs. voltage characteristics of these devices are well matched to those of the transistors in the amplifier and the temperature of all devices are very close.  This is what we did in the lab when we added the transistors connected as diodes to the Class B amplifier to change it to a Class AB amplifier.  A further improvement can be made to the circuit by converting the transistors connected as diodes to emitter follower stages, providing a high input impedance to the amplifier.  This type of arrangement is commonly called a //diamond// stage.  We can follow the bias voltage in the upper signal path as going up a V<sub>BE</sub> drop in the diode and down a V<sub>BE</sub> drop in the upper NPN transistor.  Similarly, for the lower signal path we go down a V<sub>BE</sub> drop in the diode and up a V<sub>BE</sub> drop in the PNP transistor.  Sometimes, however, this thermal compensation may not be enough to entirely avoid thermal runaway, since devices are not perfectly matched, and temperatures can vary between devices.  A heat sink, if available, can be used to help equalize the temperature among all of the devices if all of the devices are thermally connected to it.  Another technique that is often used is to place small resistors in series with the emitters of the amplifier transistors.  Doing this produces negative feedback in the same was as discussed in the "Class A NPN Common-Emitter Amplifier" lab.  This is why we placed the two 1.1 Ω resistors in series with the emitters of the two transistors.

Crossover distortion is worse than other types of distortion since it is not reduced as a percentage of signal amplitude as the signal amplitude is reduced.  Other distortion mechanisms produce harmonic distortion (distortion of the shape of a sine wave from its ideal shape) that scale with amplitude over a wide dynamic range, giving a rather constant percentage of harmonic distortion as the signal amplitude is varied.  Crossover distortion, on the other hand, does not decrease with signal amplitude -- the dead zones stay the same -- so the distortion percentage in a signal actually increases as its amplitude decreases.  Fortunately, negative feedback is often provided around amplifiers with push-pull Class AB output stages, which significantly reduces signal distortions.  Clearly, the amplifiers themselves should be designed to produce minimal crossover distortion without the negative feedback.
==== Observations and Conclusions ====
  * Ideal Class B amplifiers have conduction angles of 180 degrees
  * Two Class B amplifiers are required to amplify a sine wave -- one for each half-cycle of the sine wave
  * Two Class B amplifiers configured such that one amplifies the positive half-cycle and the other amplifies the negative half-cycle are commonly referred to as push-pull Class B amplifiers
  * Push-pull Class B amplifiers can be designed using two of the same type of transistors or two complementary transistors
  * Class B amplifiers produce significant crossover distortion, which is highly undesirable
  * A small amount of bias can be added to a Class B amplifier to form a Class AB amplifier, which has considerably less crossover distortion than a Class B amplifier
  * Single Class AB amplifiers can be combined to form push-pull Class AB amplifiers
  * Adding bias can produce thermal runaway, and avoiding the use of fixed bias sources can help avoid thermal runaway
  * Diodes, transistors connected as diodes, and emitter follower stages can be used to implement bias that has temperature compensation that reduces the likelihood of thermal runaway
  * In order to minimize the likelihood of thermal runaway, all devices should be kept at the same temperature; one way to implement this is to thermally connect all devices to the same heat sink
  * Small resistors can be placed in series with the emitters of Class AB emitter-follower amplifier stages in order to provide positive feedback in the bias circuit that can help prevent thermal runaway
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