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imported>John Stephenson |
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| In electronics, the '''[[Miller effect]]''' is the increase in the equivalent input capacitance of an inverting voltage [[amplifier]] due to a capacitance connected between two gain-related nodes, one on the input side of an amplifier and the other the output side. The amplified input capacitance due to the Miller effect, called the '''Miller capacitance''' ''C<sub>M</sub>'', is given by
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| :<math>C_{M}=C (1-A)\ ,</math>
| | <small> |
| where ''A'' is the voltage gain between the two nodes at either end of the coupling capacitance, which is a negative number because the amplifier is ''inverting'', and ''C'' is the coupling capacitance.
| | ==Footnotes== |
| | | {{reflist|2}} |
| Although the term ''Miller effect'' normally refers to capacitance, the Miller effect applies to any impedance connected between two nodes exhibiting gain. These properties of the Miller effect are generalized in '''Miller's theorem'''.
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| === History ===
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| The Miller effect is named after John Milton Miller. When Miller published his work in 1920, he was working on vacuum tube triodes, however the same theory applies to more modern devices such as bipolar transistors and MOSFETs.
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| === Derivation ===
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| {{Image|Miller effect.PNG|right|350px|These two circuits are equivalent. Arrows indicate current flow. Notice the polarity of the dependent voltage source is flipped, to correspond with an ''inverting'' amplifier.}} | |
| Consider a voltage amplifier of gain −''A'' with an impedance ''Z<sub>μ</sub>'' connected between its input and output stages. The input signal is provided by a Thévenin voltage source representing the driving stage. The voltage at the input end (node 1) of the coupling impedance is ''v<sub>1</sub>'', and at the output end −''Av<sub>1</sub>''. The current through ''Z<sub>μ</sub>'' according to Ohm's law is given by:
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| :<math>i_Z = \frac{v_1 - (- A)v_1}{Z_\mu} = \frac{v_1}{ Z_\mu / (1+A)}</math>.
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| The input current is:
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| :<math>i_1 = i_Z+\frac{v_1}{Z_{11}} \ . </math>
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| The impedance of the circuit at node 1 is:
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| :<math>\frac {1}{Z_{1}} = \frac {i_1} {v_1} = \frac {1+A}{Z_\mu} +\frac{1}{Z_{11}} .</math>
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| This same input impedance is found if the input stage simply is decoupled from the output stage, and the reduced impedance ''{{nowrap|Z<sub>μ</sub> / (1+A)}}'' is substituted in parallel with ''Z<sub>11</sub>''. Of course, if the input stage is decoupled, no current reaches the output stage. To fix that problem, a dependent current source is attached to the second stage to provide the correct current to the output circuit, as shown in the lower figure. This decoupling scenario is the basis for ''Miller's theorem'', which replaces the current source on the output side by addition of a shunt impedance in the output circuit that draws the same current. The striking prediction that a coupling impedance ''Z<sub>μ</sub>'' reduces input impedance by an amount equivalent to shunting the input with the reduced impedance ''{{nowrap|Z<sub>μ</sub> / (1+A)}}'' is called the ''Miller effect''.
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| [[Miller effect|....]]
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Latest revision as of 09:19, 11 September 2020
The Mathare Valley slum near Nairobi, Kenya, in 2009.
Poverty is deprivation based on lack of material resources. The concept is value-based and political. Hence its definition, causes and remedies (and the possibility of remedies) are highly contentious.[1] The word poverty may also be used figuratively to indicate a lack, instead of material goods or money, of any kind of quality, as in a poverty of imagination.
Definitions
Primary and secondary poverty
The use of the terms primary and secondary poverty dates back to Seebohm Rowntree, who conducted the second British survey to calculate the extent of poverty. This was carried out in York and was published in 1899. He defined primary poverty as having insufficient income to “obtain the minimum necessaries for the maintenance of merely physical efficiency”. In secondary poverty, the income “would be sufficient for the maintenance of merely physical efficiency were it not that some portion of it is absorbed by some other expenditure.” Even with these rigorous criteria he found that 9.9% of the population was in primary poverty and a further 17.9% in secondary.[2]
Absolute and comparative poverty
More recent definitions tend to use the terms absolute and comparative poverty. Absolute is in line with Rowntree's primary poverty, but comparative poverty is usually expressed in terms of ability to play a part in the society in which a person lives. Comparative poverty will thus vary from one country to another.[3] The difficulty of definition is illustrated by the fact that a recession can actually reduce "poverty".
Causes of poverty
The causes of poverty most often considered are:
- Character defects
- An established “culture of poverty”, with low expectations handed down from one generation to another
- Unemployment
- Irregular employment, and/or low pay
- Position in the life cycle (see below) and household size
- Disability
- Structural inequality, both within countries and between countries. (R H Tawney: “What thoughtful rich people call the problem of poverty, thoughtful poor people call with equal justice a problem of riches”)[4]
As noted above, most of these, or the extent to which they can be, or should be changed, are matters of heated controversy.
- ↑ Alcock, P. Understanding poverty. Macmillan. 1997. ch 1.
- ↑ Harris, B. The origins of the British welfare state. Palgrave Macmillan. 2004. Also, Oxford Dictionary of National Biography.
- ↑ Alcock, Pt II
- ↑ Alcock, Preface to 1st edition and pt III.
