Editing Negative-feedback amplifier (section)

=== Is the main amplifier block a two-port? ===
[[Image:Two-port ground arrangement.PNG|thumbnail|400px|Figure 7: Amplifier with ground connections labeled by ''G''. The feedback network satisfies the port conditions.]]
Some drawbacks of the two two-port approach follow, intended for the attentive reader.

Figure 7 shows the small-signal schematic with the main amplifier and the feedback two-port in shaded boxes. The feedback two-port satisfies the [[Two-port network|port conditions]]: at the input port, ''I''<sub>in</sub> enters and leaves the port, and likewise at the output, ''I''<sub>out</sub> enters and leaves.

Is the main amplifier block also a two-port? The main amplifier is shown in the upper shaded box. The ground connections are labeled. Figure 7 shows the interesting fact that the main amplifier does not satisfy the port conditions at its input and output ''unless'' the ground connections are chosen to make that happen. For example, on the input side, the current entering the main amplifier is ''I''<sub>S</sub>. This current is divided three ways: to the feedback network, to the bias resistor ''R''<sub>B</sub> and to the base resistance of the input transistor ''r''<sub>π</sub>. To satisfy the port condition for the main amplifier, all three components must be returned to the input side of the main amplifier, which means all the ground leads labeled ''G''<sub>1</sub> must be connected, as well as emitter lead ''G''<sub>E1</sub>. Likewise, on the output side, all ground connections ''G''<sub>2</sub> must be connected and also ground connection ''G''<sub>E2</sub>. Then, at the bottom of the schematic, underneath the feedback two-port and outside the amplifier blocks, ''G''<sub>1</sub> is connected to ''G''<sub>2</sub>. That forces the ground currents to divide between the input and output sides as planned. Notice that this connection arrangement ''splits the emitter'' of the input transistor into a base-side and a collector-side – a physically impossible thing to do, but electrically the circuit sees all the ground connections as one node, so this fiction is permitted.

Of course, the way the ground leads are connected makes no difference to the amplifier (they are all one node), but it makes a difference to the port conditions. This artificiality is a weakness of this approach: the port conditions are needed to justify the method, but the circuit really is unaffected by how currents are traded among ground connections.

However, if '''no possible arrangement''' of ground conditions leads to the port conditions, the circuit might not behave the same way.<ref>The equivalence of the main amplifier block to a two-port network guarantees that performance factors work, but without that equivalence they may work anyway. For example, in some cases the circuit can be shown equivalent to another circuit that is a two port, by "cooking up" different circuit parameters that are functions of the original ones. There is no end to creativity!</ref> The improvement factors (1 + β<sub>FB</sub> A<sub>OL</sub>) for determining input and output impedance might not work.<ref name=Jaeger2>{{cite book |title=Microelectronic circuit design |author1=Richard C Jaeger |author2=Travis N Blalock |chapter=§18.7: Common errors in applying two-port feedback theory |quote=Great care must be exercised in applying two-port theory to ensure that the amplifier feedback networks can actually be represented as two-ports |chapter-url=http://highered.mheducation.com/sites/0072320990/student_view0/chapter18/chapter_summary.html |pages=1409 ''ff''  |isbn=0072320990 |year= 2004 |publisher=McGraw=Hill Higher Education |edition=2nd}}</ref> This situation is awkward, because a failure to make a two-port may reflect a real problem (it just is not possible), or reflect a lack of imagination (for example, just did not think of splitting the emitter node in two). As a consequence, when the port conditions are in doubt, at least two approaches are possible to establish whether improvement factors are accurate: either simulate an example using [[SPICE|Spice]] and compare results with use of an improvement factor, or calculate the impedance using a test source and compare results.

A more practical choice is to drop the two-port approach altogether, and use various alternatives based on [[Signal-flow graph|signal flow graph]] theory, including the [[Rosenstark method]], the [[Choma method]], and use of [[Blackman's theorem]].<ref name=Palumbo2>
{{cite book |url=https://books.google.com/books?id=VachCXS6BK8C&q=%22Other+methods+to+analyse+feedback+amplifiers+are+based+on+Mason%27s%22&pg=PA66 |author1=Gaetano Palumbo |author2=Salvatore Pennisi |title=Feedback Amplifiers: Theory and Design |isbn=9780792376439 |publisher=Springer Science & Business Media |year=2002 |page=66}}
</ref> That choice may be advisable if small-signal device models are complex, or are not available (for example, the devices are known only numerically, perhaps from measurement or from [[SPICE]] simulations).