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The distributed amplifier is an unconventional technique that allows  
The '''distributed amplifier''' is an unconventional technique that allows  
an amplifier designer to escape the tradeoff between gain and bandwidth.
an amplifier designer to escape the tradeoff between gain and bandwidth.
 
==Problem==
With conventional amplifiers, if the gain of one stage is not enough,
With conventional amplifiers, if the gain of one stage is not enough,
the designer has to cascade stages.  The midband gain of the resulting
the designer has to cascade stages.  The midband gain of the resulting
two-stage amplifier is calculated by simply multiplying the midband gains  
two-stage amplifier is calculated by simply multiplying the midband gains  
of each of the stages.  However, the bandwidth (3dB cutoff frequency) of
of each of the stages.  However, the bandwidth (3´dB cutoff frequency) of
the two-stage amplifier is lower than the bandwidth of each of the stages
the two-stage amplifier is lower than the bandwidth of each of the stages
by itself.  In most situations the resulting risetime, <math>t_r</math>  
by itself.  In most situations the resulting rise time, t<sub>r</sub>,
is closely approximated by
is closely approximated by  
<math>t_r = \sqrt{t_{r1}^2 + t_{r2}^2}</math>, where  
:t<sub>r</sub> = (t<sub>r1</sub><sup>2</sup> + t<sub>r2</sub><sup>2</sup>)<sup>1/2</sup>
<math>t_{r1}</math> is the risetime of the first amplifier
where t<sub>r1</sub> is the risetime of the first amplifier and t<sub>r2</sub> that of second amplifier.
and  
<math>t_{r2}</math>
is the risetime of the second amplifier.


For example:
For example, cascading two amplifiers having a gain of 10 and a rise time of 3 ns, and a gain of 12 and a rise time of 4 ns, respectively, will result in a mid-band gain of 120 and a rise time of 5 ns.
 
Consider a designer who is working with a technology that produces
amplifier stages like the first amplifier in the example above.  If he needs
a total gain of 100 with a rise time of 3 ns, he/she is constrained by the
gain-bandwidth trade-off and is unable to meet both goals simultaneously.


Amplifier 1:
==Solution==
* midband gain: 10
[[File:Distributed amplifier principle.jpg|thumb|450px|right|Distributed amplifier principle]]
* risetime: 3ns
In a distributed amplifier, several stages are connected together to form what in effect
is a "transmission line with gain". The gain is the sum (not the product)
of the gains of the stages, whereas the bandwidth of a distributed amplifier is
the bandwidth of each of the stages.


Amplifier 2:
Thus, it is possible to construct an amplifier with a gain of 100 and a rise time of 3 ns
* midband gain: 12
by using ten instances of the ×10, 3 ns amplifier from the earlier example connected to
* risetime: 4ns
form a distributed amplifier.


Cascade of Amplifier 1 and Amplifier 2:
The key difference between a distributed conventional cascaded-stage amplifier is that
* midband gain: 120
in the former, the input of each stage is the original signal, not the output of a
* risetime: 5ns
previous stage, thus eliminating the cumulative degradation of rise time that occurs in
cascaded stages.


Consider a designer who is working with a technology that produces
One of the most important challenges when building distributed amplifiers is avoiding
amplifier stages like Amplifier 1 in the example above.  If he needs
reflections in the signal path.  For example, when the input signal reaches the input
a total gain of 100 with a risetime of 3ns, he is constrained by the
of one stage, parasitic capacitance of that stage must not cause an impedance discontinuity
gain-bandwidth tradeoff and is unable to meet both goals simultaneously.
in the signal path, which would cause reflection.
The solution is found in the distributed amplifier.  In a distributed amplifier
several stages are connected together to form, in effect, a transmission line
with gain.  The gain is the sum (not the product) of the gains of the stages.
The bandwidth of a distributed amplifier is the bandwidth of each of the stages.
Thus, it is possible to construct an amplifier with a gain of 100 and a risetime
of 3ns by using ten instances of Amplifier 1 connected to form a distributed amplifier.


The key difference between a distributed amplifier and a conventional amplifier
Since eliminating the parasitic capacitance is not possible, the approach is usually to
composed of cascaded stages is that in a distributed amplifier, the input of
reduce the capacitance of the transmission line around each amplifier input (thereby
each stage is the original signal, not the output of a previous stage.  This
increasing its impedance) so that the amplifier's parasitic capacitance can substitute
eliminates the cumulative degradation of the risetime that occurs in conventional
for the capacitance of that region of the transmission line.
cascaded stages.


One of the most important challenges when building distributed amplifiers is
The design of distributed amplifiers is closely related to the design of lumped-element
to avoid reflections in the signal path.  For example, when the input signal
delay lines made from L-C sections.  This, in turn, is based on the notion that a transmission
reaches the input of one stage, it is important to avoid having the parasitic capacitance
of that stage cause an impedance discontinuity in the signal path, which would cause
reflection.  Since eliminating the parasitic capacitance is not possible,
the approach is usually to reduce the capacitance of the transmission line in
the region of an amplifier so that the amplifier's parasitic capacitance can
substitute for the capacitance of that region of the
transmission line, this avoiding impedance discontinuities.  The design of  
distributed amplifiers is closely related to the design of synthetic delay lines
made from L-C sections.  This, in turn, is based on the notion that a transmission
line can be modeled as a series of L-C sections.
line can be modeled as a series of L-C sections.


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energy loss in the transmission line, which limits the number of stages.
energy loss in the transmission line, which limits the number of stages.


The following Tektronix instruments contain distributed amplifiers:
These Tektronix instruments contain distributed amplifiers:
<div style="column-count:8;-moz-column-count:8;-webkit-column-count:8">
* [[513]]
* [[513]]
* [[514]]
* [[514]]
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* [[82]]
* [[82]]
* [[945]]
* [[945]]
</div>


== Reading ==
== Reading ==
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