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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
{{:{{FeaturedArticleTitle}}}}
:<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'''.
</small>
 
=== History ===
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.
 
=== Derivation ===
Consider a voltage amplifier of gain −''A'' with an impedance ''Z<sub>&mu;</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>&mu;</sub>'' according to Ohm's law is given by:
 
:<math>i_Z =  \frac{v_1 - (- A)v_1}{Z_\mu} = \frac{v_1}{ Z_\mu / (1+A)}</math>.
 
The input current is:
 
:<math>i_1 = i_Z+\frac{v_1}{Z_{11}} \ . </math>
 
The impedance of the circuit at node 1 is:
 
:<math>\frac {1}{Z_{1}} = \frac {i_1} {v_1} = \frac {1+A}{Z_\mu} +\frac{1}{Z_{11}} .</math>
 
This same input impedance is found if the input stage simply is decoupled from the output stage, and the reduced impedance ''{{nowrap|Z<sub>&mu;</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>&mu;</sub>'' reduces input impedance by an amount equivalent to shunting the input with the reduced impedance ''{{nowrap|Z<sub>&mu;</sub> / (1+A)}}'' is called the ''Miller effect''.
{{Image|Miller effect.PNG|center|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.}}
 
[[Miller effect|....]]

Latest revision as of 10:19, 11 September 2020

Categories of smart home devices shown on Amazon's website in April 2023.

The phrase smart home refers to home automation devices that have internet access. Home automation, a broader category, includes any device that can be monitored or controlled via wireless radio signals, not just those having internet access. Whether the device is powered by the electrical grid or by battery, if it uses the home Wi-Fi network and if an internet logon needs to be created to use it, then it is smart home technology.

Collectively, all the smart home devices on every home's Wi-Fi network helps to make up what is called the Internet of Things (IoT), a huge sea of sensors and control devices across the world that are capable of being accessed from afar via the internet. One of the key reasons such devices need internet access is so that the manufacturer can periodically download updated firmware to the device to keep it up-to-date. However, being available via the internet also means that such devices are, potentially, available for spying or hacking. Today, homes may contain dozens or even hundreds of such devices, and consumers may enjoy their benefits while knowing little about how they work, or even realizing that they are present.

Not all home automation is "smart"

Many remotely controllable devices do not require internet access. They may instead have physical control devices that use either RF (“Radio Frequency”) or IR (“Infrared”) beams, two different kinds of energy used in remote controls to communicate commands. Non-"smart" home automation may also present security risks, because the control signals can be hijacked by bad actors with the right signaling equipment. Garage door openers are of particular note in this regard. Modern automobiles, in fact, are full of automation similar to home automation, and cars are hackable by bad actors in a number of ways. See Wikipedia's Automotive hacking article for more information.

Incompatibility hassles

At present, consumers must make sure that the smart device they wish to use is specified to be compatible whichever phone/tablet operating system they use (Apple vs. Android). Since smart home products emerged in the absence of any standard, a morass of competing methods for networking, control and monitoring now exist. For some products, consumers may need to buy an expensive hub, or bridge, a device that is specific to one vendor. Products made by different manufacturers but performing the same function are typically not interoperable. Consumers often need to open a different app on their smartphone or tablet in order to control devices by each manufacturer. This may make it too expensive and awkward to try out competing devices, leaving consumers stuck with the product they bought originally or else having to add yet more apps to their phones.

Security concerns

Security for smart home products has been uneven and sometimes seriously inadequate. Smart thermostats which can monitor whether a home's occupants are present or not, entry-way locks, robotic vacuums that work with a map of the house, and other smart home devices can present very real dangers if hackers can access their data.

Matter, an emerging standard

Matter is emerging standard in 2023 intended to increase security, reliability and inter-operability of smart-home devices. About ten years ago, industry consortiums formed to work on standards for smart home device communications, and their underlying wireless communications, which would make it possible for products from all vendors to work together seamlessly and provide fast performance, privacy, and security and would work even if there is not connection to the outside internet (i.e., no connection to "the cloud" or to servers).

Footnotes