page_title: Negative-feedback amplifier
section_title: Is the main amplifier block a two-port?
hierarchical_section_title: Negative-feedback amplifier / Two-port analysis of feedback / Is the main amplifier block a two-port?
caption_attribution_description: Ground connections in feedback amplifier
context_page_description: A Negative-feedback amplifier is an electronic amplifier that subtracts a fraction of its output from its input, so that negative feedback opposes the original signal. The applied negative feedback can improve its performance and reduces sensitivity to parameter variations due to manufacturing or environment. Because of these advantages, many amplifiers and control systems use negative feedback.
  An idealized negative-feedback amplifier as shown in the diagram is a system of three elements:
  an amplifier with gain AOL,
  a feedback network β, which senses the output signal and possibly transforms it in some way,
  a summing circuit that acts as a subtractor, which combines the input and the transformed output.
context_section_description: 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 port conditions: at the input port, Iᵢₙ enters and leaves the port, and likewise at the output, Iₒᵤₜ 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 IS. This current is divided three ways: to the feedback network, to the bias resistor RB and to the base resistance of the input transistor rπ. 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 G₁ must be connected, as well as emitter lead GE1. Likewise, on the output side, all ground connections G₂ must be connected and also ground connection GE2. Then, at the bottom of the schematic, underneath the feedback two-port and outside the amplifier blocks, G₁ is connected to G₂. 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. The improvement factors (1 + βFB AOL) for determining input and output impedance might not work. 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 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 theory, including the Rosenstark method, the Choma method, and use of Blackman's theorem. 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).
caption: Figure 7: Amplifier with ground connections labeled by G. The feedback network satisfies the port conditions.
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