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If we take a transistor (bipolar or
MOS), a light emitting device made form GaAlAs, GaP,
whatever, a Laser diode, a simple rectifying diode (pn-junction or
Schottky junction), i.e. just about any device made from semiconductors, we may
modulate any of its input parameters (either a little bit or a lot), and see
what happens to all other parameters. The paradigmatic experiments, of course
are |
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MOS
transistors: Modulate the gate voltage, see what the source-drain
current does. |
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Bipolar
transistors: Modulate the base current, see what the
emitter-collector current does. |
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Rectifying
diodes: Modulate the terminal voltage, see what the device current
does. |
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Solar cell:
Modulate the light flux, see what the photo current or the photo voltage
does. |
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Light emitting
diodes: Modulate the injection current, see what the light output
does |
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Laser diodes:
Modulate the pumping (i.e. the injection current), see what the light output
does. |
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The list could be expanded, and many variants are
possible. |
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Generally, we have highly non-linear
systems and a simple sinus modulation of the input parameter In
in the form of |
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| In(t) = In0 +
Inm · sin (w · t)
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Or, expressed more generally using complex
notation |
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| In(t) = In0 +
Inm · exp (i · w ·
t) |
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This simple input function, however, in general, will produce responses that are no
longer sinus shaped, but contain higher harmonics. |
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It is thus useful to distinguish
between two basic modes of frequency
responses, illustrated below for a simple rectifying diode. |
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As long as the input modulation
is kept small, the response will be linear.
This is called the small signal
response or behavior. |
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Large modulations or signals then obviously give
the (non-linear) large signal
response. |
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Shown is the small signal response on the left,
and the large signal response on the right. Note that the reponse in any case
is directly given by the shape of the I-U characteristic and thus
is not directly dependent on the
frequency. |
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That, however, must be an
oversimplification. At high frequencies we must expect deviations from the
1:1 correspondence of input and output via the characteristics, and it
this behavior we after. Still, the distinction between small signal and large
signal behavior (or linear and non-linear response) is still valid. |
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The distinction between the two cases
is simple: As soon as you find significant deviations in the form of the output signal from the from that of the
input signal, you have the large signal case. |
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In other words: You have the
small signal case, if for an input signal
In(t) = In0 + Inm ·
exp (i · w ·t) your output
signal can be adequately described by |
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| O |
= |
O0 +
Om · exp (i · [w ·
t + j)] |
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| Om |
= |
V · Inm |
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| V |
= |
Amplifikation = |
dI/dU |
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| j |
= |
arbitrary phase shift |
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Note that for a given input signal, it may depend
very much on the choice of the the working or operating point, if you observe
small signal, or large signal behavior. |
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While digital real devices usually operate in the large
signal mode (the current/voltage is either on or off with the largest possible
amplitudes the system permits), we are only going to look at small signal behavior here. |
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Generally, we are now entering the very large
world of electronic engineering and system analysis, but here we will only ask
ourselves one question: What constitutes the basic
limits of frequency response for the paradigmatic "ideal" devices as listed
above. |
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A real device
- always coming with wires, series resistances, parasitic capacitors and
inductors, and in most cases consisting of many connected single devices -
might have a quite different frequency response; but it is always determined by
the frequency response of its individual elements. |
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Generally, we expect that for small frequencies
w at the input, the output will have no
problem following the input. |
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Contrariwise, for high frequencies, the device
will be to sluggish, and the output amplitude must decrease with frequency
until there is practically no more response. |
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What we are interested in are answers
to the following questions: |
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What is the general (small signal) frequency
response of a given basic devices as listed above? |
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What are the important factors, in particular
material properties, that determine the
maximum usable frequencies; and what kind of specific frequency response curve
do we obtain? |
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What can we do about it? How can we optimize
frequency response; i.e. how must we design materials and devices usable at
very high frequencies? |
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This is not going to be easy. There
are several mechanisms that influence "device
speed" and their combined effects may result in complex
behavior. |
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In what follows we will first look at some
general mechanisms that might limit device speed and than apply this to some
specific devices. |
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© H. Föll
