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T r a n s i s t o r s

Introduction Animations Differential Amplifier
Fundamentals Common Base Stage  CMRR  Common Mode Rejection Ratio
Gain =  Hfe = Beta  Common Collector Stage  Gain Bandwidth Product
D.C. Coupled  Darlington Pair Miller Effect
A.C. Coupled Emitter Follower Bypassing Supply Rail   (LINK)
V to I Convertor  Voltage Regulator High Frequency Compensation
I to V Convertor A.C. Feedback  Input Impedance 
Bias D.C. Feedback Output Impedance
Clipping & Cutoff Thermal Feedback   
Common Emitter Stage  Video Amplifier  
[Load Based Analysis of Transistors]-... [FETs]


    Introduction 
The purpose of this page is to try and explain the transistor. 
The audience to which it is aimed, is anyone who has or hasn't a clue to how these little Buggers  work and/or how to use them. A real problem with some other explanations: for the sake of "fidelity" authors' include confusing details until the concept, or thread--of how they actually work & how to use them--is lost. 

No claim to scholarship is made, but you may end up knowing just a little more than before--or NOT! 

The following is comprised of several different explanations. They should be read several times, because any insight gained from one may help in understanding another. The "List of Characteristics" should be read for parts of the puzzle, not for insights: however, "you-takes-what-you-gets."

  Good luck,
           glen

-A Transistor is a Current In/Current Out Device-
A Transistor can be thought of as a device that is active in only One Direction:  It can draw more or less current through its load resistor (sometimes referred to as a pull-up resistor). 

 It can either Source Current or it can Sink Current, it Cannot do Both.-
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Since the Transistor is a Current device, any signal Voltage must first be 
Converted to a Current.
  Voltage to Current Convertor 
First, you must convert the input voltage to a current by 
using a Voltage to Current Convertor--a resistor.
Since the Transistor is a Current in/Current out device, any Current Output is 
Converted to a Voltage Drop by the Current flowing thru a Load Resistor.

  Current to Voltage Convertor
Next, you convert the output current into a voltage by 
using a Current to Voltage Convertor in the collector circuit--you  guessed it--a resistor.
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Mouse-Over image to see Animation
Note voltage to current convertor in the base circuit.  A.K.A., current limiting resistor.
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Mouse-Over image to see Animation
Results of driving a transistor's base directly from a voltage 
source, with no voltage to current convertor, i.e., a resistor.
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A N I M A T I O N S
If a picture is worth 1024 words, how many words if it moves?
Click-it  to make it Bigger
Spring as Load Analogy
Common Emitter
 Common Base
     
Differential Amplifier
Differential input
Common Mode input
Transistor Models-
The Rheostat as a Transistor
The transistor can be thought of as a device that is like a rheostat (potentiometer). If you think of a pot tied to a fixed resistor as a transistor amplifier: the pot is working against the fixed resistor--the collector load resistor. This means the transistor cannot generate a positive and a negative signal, it can only draw more or less current, e.g., the pot decreases its resistance, causing more current through the "load" resistor, thus causing the voltage dropped across that resistor to increase; the pot increases its resistance, causing less current through the load resistor, and this causes less voltage to be dropped across the load resistor. If we think of the extremes of current as being the equivalent of the positive and negative alternations of a sine wave, then it follows that the equivalent of zero is some current equidistant between the two. 
There's an Echo in Here
A NPN transistor connected as a common emitter amplifier: the base needs current to do its thing. 
The collector cannot output voltage, it can only cause more or less current to be drawn through its load resistor. If a voltage is applied to the base resistor a current now flows into the base (base emitter junction). If a resistor is connected between the collector and a positive supply voltage: the collector current flowing through the collector or load resistor causes a voltage to be dropped across said load resistor. 
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Diodes as Transistor
We can simulate a NPN transistor using two diodes and connecting both anodes together. One cathode is tied to common (the emitter); the other cathode (the collector) goes to a load resistor tied to the positive supply. Now connect a 1k resistor to the junction of the two anodes (the base), and using a signal generator, apply a 0 to 2 volt P-P sine wave to the other end. Using a dual beam oscilloscope, observe the signal at both ends of the resistor, i.e., the generator and the "base." 
 
The results should resemble the figure: the diode signal starts up unimpeded until it reaches ~ 0. 6 volts peak (1.2 volts P - P), at which point the voltage at the "base" appears to stop increasing, even though the signal generator is still increasing in amplitude. No matter how much the voltage applied from the generator increases (within reason), the "base" voltage appears to not increase. However, the current into that junction (two anodes) increases linearly: I = [E - 0.6]/R. 
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Now at this point, the analogy falls apart: these two diodes have no gain, as the transistor we are trying to simulate would have. However, let us pretend that it does: the "collector" is a high impedance current source and if a resistor (the load resistor) is connected between the "collector" and the positive supply, a voltage is seen at the collector. This changing voltage drop across the resistor--caused by the changing collector current--will change correspondingly to the "base" current. 

Now follow me, just a few more words, and You've got it! As the voltage at the generator goes more positive; the base current increases; the collector current increases; the voltage drop across the collector resistor increases; and the voltage at the collector goes less positive or lower. 

Hang on! Stay with me! 
Conversely, when the voltage at the generator goes less positive; the base current decreases; the collector current decreases; the voltage drop across the collector resistor decreases; and the voltage at the collector goes more positive or higher. Feel better now OK, So I Lied: There is just a little more to the story. Remember when the base reached ~0.6 volts? well the collector output is only that part of the signal that caused the base to conduct current. In other words: until the base rises to ~ 0.6 volts and there is base current, there is no change at the collector--no collector output.
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Make a List 
The following list of attributes may, at first glance, seem confusing and contradictory, however they are all true and are offered as clues to the puzzle of: 'how does a transistor really work?' 


Abstractly, here are some Characteristics:

  1. An equivalent circuit of a NPN transistor is two diodes tied anode to anode; one cathode being the emitter, the other the collector, and the junction of the anodes is the base.

  2. When a NPN transistor is doing-its-thing, there is always a constant 0.6 volt drop between the base and emitter, i.e., the base is always ~ 0.6 volts more positive than the emitter--always!

  3. There is no output at the collector, until the base has reached ~ 0.6 volts and the base is drawing current, i.e., any signal that appears at the base that is not up to ~ 0.6 volts (and not drawing base current), is never seen at the collector. 

  4. The base requires a current, not a voltage to control the collector current. 

  5. The collector is a current source: it does not source a voltage. 

  6. The collector appears to output a voltage when a resistor is connected between it and power. 

  7. The collector is a high impedance when compared to the emitter. 

  8. The transistor can output an amplified signal either from the collector or the emitter (or both). 

  9. When operating with a collector resistor (RL): the output voltage from the collector is an amplified voltage. 

10. When operating with only an emitter resistor (Re): the output voltage from the emitter is not an amplified voltage, because it is always ~ 0.6 volts, below the input (base) voltage--hence the name voltage follower. But because the emitter can source large amounts of current to the "LOAD," it can be said, there was CURRENT amplification.

11. The collector--being high impedance--cannot drive a low impedance load. 

12. The emitter--being a low impedance--can drive a low impedance load. 

13. The voltage gain from the collector is greater than one (Gv > 1). 

14. The voltage gain from the emitter is less than one (Gv < 1). 

15. Both the collector and the emitter: output ~ the same power: E x I = P. 
 

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One More Explanation of How a Transistor Works.
Mouse-Over image to see Animation
Because a transistor is a current device: if you cause some current to flow in the base, a larger amount of current is caused to flow in the collector. There's that pesky echo again. 

Looking at the common emitter circuit in the figure: while measuring the voltage and the current, one starts to apply a voltage to the base of the transistor through the base resistor.

As the voltage increases from, zero there is no current flowing. At 0.1 volt, no current; 0.2 volt, no current; 0.5 volt, still no current; as the voltage at the base approaches 0.6 volts--where there was no current--all of a sudden a small current starts to be drawn by the base, and the voltage at the base slows its rate of increase--and remains at ~ 0.6 volts. As the voltage from the source increases, the voltage at the base remains ~ 0.6 volts, and the current increases--as well as the corresponding collector current.
At some point, as the currents increase, the increase in the collector current starts to slow, until it stops increasing altogether, at this point it is said to be in Saturation (if this transistor was being used as a switch or as part of a logic element, then it would be considered to be switched on). 
Mouse-Over image to see Animation
Mouse-Over image to see Animation
Mouse-Over image to see Animation

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What have we learned? 
First, as the input voltage is increased from 0 volts towards 0.6 volts, there is an abrupt change in current, i.e., from zero current to some small current flow. Just below this point where there is no current flow, the device is said to be in Cutoff. This low end region is considered a nonlinear part of the operating curve (see the curves). Next, consider the other extreme: as the currents in the base and collector are increasing (base and collector are tracking), and the collector current is starting to no longer track the input base current: this too is considered a nonlinear part of the operating curve, and is in saturation (again refer to the curves). 
Direct Coupled Amplifier  (A.K.A., D.C. Coupled)

Common Emitter Amplifier
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Now, to the heart of the matter!
We have an operating curve consisting of a fairly linear segment bounded by two nonlinear ends: cutoff and saturation. 

Operating in the Middle
The transistor will operate very nicely if one could insure that no input voltage, i.e., signal voltage--would cause the collector current to ever operate beyond either end of the linear portion of the operating curve. 

Base Current verses Collector Current
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Sorry, But I Have a Bias
Along comes bias. You have heard about it, you've read about it, you may have even dreamed about it: now is your chance to see-for-yourself--up close and personal. Before one applies a signal voltage to the base circuit, an arrangement for a steady voltage to be applied to the base, such that--with no input signal--the collector current is the same as when it is about half way up, or center of--the linear part of the curve. Now if we apply, say, an AC sinusoid to the base circuit (through a capacitor), the collector current--when seen as a large AC signal voltage at the collector--will be linear and undistorted. 
A.C. Coupled Amplifier
Common Emitter Amplifier
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Hit 'em Again, While He's Down
To further beat a point into the ground: if one increased the input signal beyond this level, the output signal would now start to "Clip" and cause distortion (sine wave gets flat on top and/or bottom). If the bias point were set either too low or too high, then the sine wave would start to clip on the top before the bottom, or visa versa (asymmetric clipping). 
A.C. Coupled Amplifier
Common Emitter Amplifier
Hint #31, Active in Only One Direction
The transistor can be thought of as a device that is active in only one direction: it can draw more or less current through its load resistor. In the case of a NPN transistor tied as a common emitter amplifier: the device can only actively sink current through the load resistor (otherwise known as a pull-up resistor) it cannot source current. 
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    Effects of different Bias Settings 

Near Cutoff Linear Portion Near Saturation
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Let Me Count The Ways
By now you have probably guessed that there are several other ways to "hook-up" the transistor. In the previous 3 volumes we have discussed using the, so called, common emitter amplifier: where the only output is at the collector. Now we will introduce you to an interesting arrangement: the common collector, otherwise known as an Emitter Follower, or voltage follower. 
Now gang, this is where it gets sticky:
The definition of an "ideal" voltage source is a source having zero output impedance, i.e., infinite current can be drawn, and the voltage stays the same. 

Where the common emitter amplifier required a voltage to current convertor for its current input requirement, this configuration requires voltage input only.

And because there is always a ~ 0.6 volt offset between the base/emitter junction (as did the common emitter), the emitter sources a voltage that reflects the input voltage, minus this offset, times the voltage gain: 
Vout = [Vin - 0.6 volts] x [Gv = .95]. 

Emitter Follower
A.K.A., Common Collector
Lets see if I have this right: "Voltage in, voltage out; and it's a current Amplifier?" 
Bingo! Think about it: 

1) The voltage-in is not amplified (Gv ~ .95);

2) There is impedance transformation--high to low; there is power amplification: Therefore there must be current amplification. 

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Some other attributes are:
It has a voltage gain of less than one (Gv ~ .95); it is not easy to cutoff, or saturated the transistor. Unlike the common emitter, it does not invert the polarity of the input signal; it is among the most stable of amplifiers--yes it is an amplifier, even if it has a voltage gain below one. Because it has high input impedance, and low output impedance, it is often used for transforming a high impedance output, to a low impedance output: it is often used to drive transmission lines, e.g., video cable from camera to monitor. Also, it is often used as the output stage (pass transistor) of linear voltage regulators. If a 5.6 volt voltage source (low impedance) is connected to the base, the emitter output will try to maintain that voltage minus 0.6 volts: 5.60 - 0.6 = 5.0 volts (how well it maintains this voltage is dependent on the transistor's gain: Hfe = large number). 

Another attribute is its excellent high frequency response. Because there is no voltage gain, or because it has a gain of ~ 1, the bandwidth is equal to the cutoff frequency of the transistor,  Ft (where Ft = [Hfe = 1]: BW = Ft).

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Note: because there is no voltage gain, there is no multiplication of the base/collector capacitance (Co) which reduces the high frequency response of common emitter amplifiers; see, also: Miller effect
Why a Voltage Gain of Less-Than-One? Good question. 
Here goes! In an emitter follower configuration, as voltage equal to--or greater than--0.6 volts is applied directly to the base, a current is caused to flow through the the emitter resistor resulting in a commensurate voltage drop. This voltage drop is always equal to the input minus ~0.6 volts multiplied by some value slightly less than one. e.g., .95. 

In the previous common emitter amplifier the current into the base was determined by the relative difference between the base and emitter--above 0.6 volts. 

In the case of the emitter follower, as the base voltage is increased, there is a corresponding tracking of the base/emitter differential: the emitter rises to--or follows--the base's change. If the output follows the input, there can never be enough current drawn by the base to cause a voltage drop across the emitter which exceeds the input voltage--hence no voltage gain. This is an elegant case of (internal) negative feedback

The amount of base current required to cause some larger current to flow through the emitter resistor (and corresponding voltage drop) is dependent on the gain--Hfe--of the transistor and the emitter load (emitter resistor and load).

Another way of thinking about this relationship, is as input impedance: if the transistor had infinite gain, there would be no base current, resulting in infinite input impedance.

If the transistor had zero gain, the input impedance would be directly dependent on the emitter resistor, i.e., base current = emitter current. 

If the transistor had some finite gain, the input impedance would be finite, i.e., base current would be dependent on the emitter resistor modified by the transistor's finite gain (Hfe), i.e., base current ~= emitter current/Hfe. 

In all of this, one can think of it as a sort of internal feedback, or bootstrapping of the input impedance. 

Why is an emitter follower so stable? Another good question. Easy to answer: As long as the gain is 1 or less than 1, it can never oscillate. Oscillation requires a positive feedback and a gain of greater than 1 to sustain oscillation (of which instability is a precursor).

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That Pair's DARLINGton 
The maximum input impedance one can expect from an emitter follower, is limited by the finite gains of individual transistors (~ 50 to ~ 350). However, there is a way to increase the effective gain or transistors by using two transistors. The total gain of this transistor pair is Gv1 x Gv2 = Gv total (Gv ~ 2k - 100k). This is achieved by arranging the transistors such that the emitter of one is driving the base of the next and connecting the collectors together. This is known as a Darlington pair, and can be used as any single transistor would be: common emitter, emitter follower, etc. 

The down side of this arrangement, is reduced speed: because of the very high gain's effect on the collector to base capacitance, Co (Ctotal = Co x Hfe). 

Darlington Pair

High Input Impedance, 
Very High Gain Stage

An Ideal Amplifier 
An ideal amplifier is one that is made up of some gain device (transistors) that has very much more gain than the finished amplifier. If this gain device had infinite gain, then the amplifier's gain would be completely dependent on the gain setting resistors: which set the gain by determining the amount of feedback used to overcome the amplifier's open loop gain (e.g., Op Amps). In the case of simple single transistor gain stages, the control exerted by the gain setting resistors is limited and has less effect on the stage's overall performance, i.e., the transistor's inherent gain is dominant. However, realize that the greater the ratio of final amplifier gain to the maximum possible gain (no feedback) of the transistor, the less vulnerable the gain of the amplifier is to variations of the individual transistor's gain (within limits).

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A.C. Coupled Common Emitter Amplifier

No Feedback
A Common Emitter Amplifier Without Feedback
A simple common emitter transistor amplifier--having no negative feedback--is not an ideal amplifier. This is because of the variability of gain from one transistor to another making uniform gain from amplifier to amplifier impossible. Also, without feedback some amplifiers--having transistors with excessive gain--might be unstable and prone to be oscillate, as well as, poor signal to noise and distortion ratios (S/N+D); low input impedance (poor impedance matching between stages, etc.), and susceptibility to temperature extremes. Without negative feedback, high ambient temperatures can raise the operating point, thus heating the device further; ending with this positive (thermal) feedback, bringing on the transistor's permanent failure.

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Phase Invertor
So That's Feedback, ah... 
When (negative) feedback is introduced, most of these problems diminish or disappear, resulting in improved performance and reliability. There are several ways to introduce feedback to this simple amplifier, the easiest and most reliable of which is accomplished by introducing a small value resistor in the emitter circuit. The amount of feedback is dependent on the relative signal level dropped across this resistor, e.g., if the resistor value approached that of the collector load resistor, the gain would approach unity (Gv ~ 1). 

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Emitter and Collector Feedback
And to beat a simple point into Terra firma: with no emitter feedback (no Re), the gain would be essentially that of the transistor. 

Another feedback technique is the introduction of some fraction of the collector signal back to the base circuit. This is most easily done via the positive biasing resistor (Rb1) --as in the figure. A third --but by no means last --approach is to use a combination of feedback techniques. 

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The Miller Effect
It's Miller Time
In a gain stage (common emitter) there is a limit to the achievable bandwidth at some set gain: i.e., the higher the gain, the lower the bandwidth; conversely, the lower the gain, the wider the bandwidth. This is the now famous, Gain Bandwidth Product. The dominant mechanism for this is found in the intrinsic feedback capacitance, Ccb, between the collector and the base. The effect--as frequency increases--is to increase feedback via Ccb's capacitive reactance, XCcb, thus reducing the overall gain. To compound this problem: XCcb is dependent on the intrinsic capacitance, Ccb, multiplied by the gain, i.e., as the gain is reduced, the bandwidth is increased. There are ways of reducing this effect, such as peaking coils in the collector (Xl cancels Xc); pre-emphasis of the signal's higher frequencies at the input; frequency selective feedback, etc...

The Miller Effect
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Gain Bandwidth Product
Using several lower gain stages in cascade is a strategy that also works. And, a very direct and effective solution is a common base configuration, in which the input signal drives the emitter, and the base is grounded, which has the effect of breaking the collector/base feedback path. Frequency dependent feedback In the figure, the capacitor, Ce, across the emitter resistor, Re, causes the gain of this device to be greater at higher frequencies. As capacitive reactance, Xc, approaches the value of Re, a rapid increase in gain occurs. The effect, of course, is to reduce the negative feedback at higher frequencies. This is often done to compensate for the limited bandwidth of the transistor stage. 
Common Base Stage

Because the base is "grounded", this configuration does not suffer from the Miller Effect, thus yielding the widest bandwidth of all configurations. Note that the drive is to the Emitter, and there is no signal inversion.

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Video Amplifiers
A video amplifier is used to amplify video from TVs, cameras, computer graphic devices, etc. Aside from having sufficient bandwidth and the ability to drive long cables: they cannot invert the signal's polarity; if they did: unless you were using an even number of amplifiers in cascade, the image would end up a negative. If you wanted a gain stage, but didn't want the signal to be inverted, you would drive the emitter instead of the base. This works, but as you might imagine, the input impedance is quite low. So by using what we learned about emitter followers back in chapter 219, we can "transform impedances," and now the noninverting video amplifier looks better. 
Non-Inverting Video Amplifier

High Frequency Compensation: Ccp
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The Differential Amplifier
Differential amplifiers are everywhere: input stages of Op Amps; comparator inputs; some video amps; balanced line receivers for digital data transmission ; etc... It is not one of the more easily understood combinations of transistors, however, I shall attempt to explain this "not-so-little-bugger." 

A differential amplifier is an amplifier that has two inputs, each of which is sensitive to the opposite polarity of the other, i.e., if the inverting input has a positive going signal, and the non-inverting input has the negative version, then there is an output equal their difference (multiplied by some gain, Gv). Conversely, if both inputs happen to be at the same value, then there is no output signal: they cancel one another, i.e., both signals (being the same polarity and amplitude) make no change is the shared emitter resistor's current, therefore, neither signal affects the other: there is "cancellation," otherwise known as Common Mode Rejection, CMR. Another way of saying the same thing is: if both inputs have the opposite polarity (or phase) signal, the shared emitter resistor draws current equal to the algebraic summation of both transistors. 

Deja vu All Over Again
You may have noticed that the configuration of the transistors in a differential amplifier are a combination of common emitter and emitter follower. OK? OK. 

 
OK, Point #1:
A signal into either input's base, causes an inverted signal at its collector, and simultaneously, a smaller, non-inverted output at the (shared) emitter resistor.

OK, Point #2:
Any signal at the emitter will appear at the collector as a non-inverted version of this signal--but amplified (remember the video amp?). 

OK, Point #3: 
Therefore, any signal at one transistor's input is not only seen at its collector, but is also seen at the other transistor's collector, enabled by the action of the shared emitter resistor (Points #1 & #2). 

What, Not a Restatement of the Same Old Thing!
This amplifier consists of two or three transistors (two in the simple version, three or more in the more precision version). These two input transistors are coupled to each other, via each's emitter, and share the same emitter resistor . At this common connection each input transistor affects the output of itself, as well as, the other transistor's output. 
 

"I Lied." Or Did He? Now that you think you understand how a "Differential Pair" works, there is just a little more to the story. Previously I said that the two input transistors share the same emitter resistor, leaving the impression that a signal voltage was at the junction of the emitters and Re. If you think about it, when one transistor is increasing in current, e.g., positive alternation of a sine wave; the other transistor is decreasing in current, by an equal amount, for the negative alternation. Since the pair is sharing the one resistor, one can deduce that, ideally, there is always a constant current in that resistor. Ideally, it is desired that the emitters transfer all of their signal to the other transistor's emitter. 
Click Me!

see a constant current source
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Enter the Oft-Maligned Constant Current Source 
Because of a non-ideal world and the non-ideal transistors that cohabit it, a constant current source (generator) is substituted for Re. A constant current generator is a circuit in which a fixed voltage source (Zener diode) is applied to the base, along with some current determining resistor in the emitter circuit. The result is a collector that will furnish a constant current over a wide range of voltages. 
On the Level -----------------------------------------
Differential stages are also useful for level translation. Either input can be driven (biased) to affect the operating point of both transistors in a complementary fashion, and therefore the output (collector) offset voltage. This is what allows the Op Amp's offset voltages to be trimmed to zero. (See figures) 
 

Don't lose your Temperature
As mentioned, one of the features of a differential amplifier is its ability to reject common mode signals (CMRR), i.e., if the same signal is on both inputs in equal amounts the output does not change. This works because of "common" signal cancellation that occurs within that first differentail stage, between the inverting & non-inverting inputs. The degree of precision of this effect is dependent directly on how closely the two transistors are matched (gain, etc.). Typically both transistors share the same substrate and/or package; these appear as one transistor but are, in fact, a pair--sometimes refereed to as a "differential pair."

As you might guess, when packaged like this, they also share the same temperature gradients. However, if the two transistors are separated, the slightest change in temp that is not shared can cause a large shift in offset voltages as seen at the output (e.g., between both collectors). This might appear as a change in gain, but it is really more a "shift" in its quiescent voltages. However, if there is any cancellation going on, this shift might reduce the cancellation which would appear as a change in gain...



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