Miller theorem
There is also a dual Miller theorem with regards to impedance supplied by two current sources connected in parallel.
The theorems are useful in 'circuit analysis' especially for analyzing circuits with feedback[1] and certain transistor amplifiers at high frequencies.
The Miller theorem establishes that in a linear circuit, if there exists a branch with impedance
The Miller theorem implies that an impedance element is supplied by two arbitrary (not necessarily dependent) voltage sources that are connected in series through the common ground.
was just grounded), the input current flowing through the element would be determined, according to Ohm's law, only by
The proportion between the voltages determines the value of the obtained impedance (see the tables below) and gives in total six groups of typical applications.
The circuit impedance, seen from the side of the output source, may be defined similarly, if the voltages
Most frequently, the Miller theorem may be observed in, and implemented by, an arrangement consisting of an element with impedance
Depending on the kind of amplifier (non-inverting, inverting or differential), the feedback can be positive, negative or mixed.
But Miller theorem is not only an effective tool for creating equivalent circuits; it is also a powerful tool for designing and understanding circuits based on modifying impedance by additional voltage.
and amplifiers with series negative feedback (emitter degeneration), whose input impedance is moderately increased.
Examples are potentiometric null-balance meters and op-amp followers and amplifiers with series negative feedback (op-amp follower and non-inverting amplifier) where the circuit input impedance is enormously increased.
Negative impedance obtained by current inversion is implemented by a non-inverting amplifier with
Zeroed impedance uses an inverting (usually op-amp) amplifier with enormously high gain
The circuit behaves as a short connection and a virtual ground appears at the input; so, it should not be driven by a constant voltage source.
For this purpose, some circuits are driven by a constant current source or by a real voltage source with internal impedance: current-to-voltage converter (transimpedance amplifier), capacitive integrator (named also current integrator or charge amplifier), resistance-to-voltage converter (a resistive sensor connected in the place of the impedance
The inverting integrators from this list are examples of useful and desired applications of the Miller effect in its extreme manifestation.
In all these op-amp inverting circuits with parallel negative feedback, the input current is increased to its maximum.
A typical application is a negative impedance converter with voltage inversion (VNIC).
The original Miller effect is implemented by capacitive impedance connected between the two nodes.
But modifying properties of Miller theorem exist even when these requirements are violated and this arrangement can be generalized further by dynamizing the impedance and the coefficient.
Besides impedance, Miller arrangement can modify the IV characteristic of an arbitrary element.
The circuit of a diode log converter is an example of a non-linear virtually zeroed resistance where the logarithmic forward IV curve of a diode is transformed to a vertical straight line overlapping the
converge to ground, we can replace this branch by two conducting the referred currents, with impedances respectively equal to
Dual Miller theorem is usually implemented by an arrangement consisting of two voltage sources supplying the grounded impedance
Depending on the kind of the amplifier (inverting, non-inverting or differential) and the gain, the circuit input impedance may be virtually increased, infinite, decreased, zero or negative.
As the main Miller theorem, besides helping circuit analysis process, the dual version is a powerful tool for designing and understanding circuits based on modifying impedance by additional current.
Typical applications are some exotic circuits with negative impedance as load cancellers,[6] capacitance neutralizers,[7] Howland current source and its derivative Deboo integrator.
As a result, the total current flowing through the load is constant and the circuit impedance seen by the input source is increased.
Below is a list of circuit solutions, phenomena and techniques based on the two Miller theorems.
