hey guys,
i modified my AGP-slot to an PCI-E
he electromagnetic spectrum is the range of all possible electromagnetic radiation. Also, the "electromagnetic spectrum" (usually just spectrum) of an object is the range of electromagnetic radiation that it emits, reflects, or transmits.
The electromagnetic spectrum, shown in the table, extends from just below the frequencies used for modern radio (at the long-wavelength end) to gamma radiation (at the short-wavelength end), covering wavelengths from thousands of kilometres down to fractions of the size of an atom. It is commonly said that EM waves beyond these limits are uncommon, although this is not actually true. The 22-year sunspot cycle, for instance, produces radiation with a period of 22 years, or a frequency of 1.4*10-9 Hz. At the other extreme, photons of arbitrarily high frequency may be produced by colliding electrons with positrons at appropriate energy. 1024 Hz photons can be produced today with man-made accelerators. In our universe the short wavelength limit is likely to be the Planck length, and the long wavelength limit is the size of the universe itself (see physical cosmology), though in principle the spectrum is infinite.
Electromagnetic energy at a particular wavelength λ (in vacuum) has an associated frequency f and photon energy E. Thus, the electromagnetic spectrum may be expressed equally well in terms of any of these three quantities. They are related according to the equations:
\lambda = \frac{c}f \,\!
and
E=hf \,\!
or
E=hc/\lambda \,\!
where:
* c is the speed of light, 299792458 m/s (c \approx 3 \cdot 10^8 \ \mbox{ m}/\mbox{s} = 300,000 \ \mbox{km}/\mbox{s}).
* h is Planck's constant, (h \approx 6.626069 \cdot 10^{-34} \ \mbox{J} \cdot \mbox{s} \approx 4.13567 \ \mathrm{\mu} \mbox{eV}/\mbox{GHz}).
\hat K_j (1) f(1)= \phi_j(1) \int { \frac{\phi_j^*(2)f(2)}{r_{12}}dv_2}
where \hat K_j (1) is the one-electron Exchange operator,
f(1),f(2) are the one-electron wavefunction being acted upon by the Exchange operator as functions of the positions of electron 1 and electron 2,
φj(1),φj(2) are the one-electron wavefunction of the j-th electron as functions of the positions of electron 1 and electron 2,
r12 is the distance between electrons 1 and 2.
out = νEc + ρEs
Ec = AEi
Ei = βEc + ξEs
The model is maybe called "Black's model".
Here Es is a source quantity and Eout is an output quantity. In electronics, each of Es and Eout can be either a voltage or a current.
Since we are dealing with physical quantities, β * A is dimensionless. ρ has the same dimension as ξ * A * ν.
Now, a feedback amplifier consists of a gain part and a feedback network. The (usually passive) feedback network makes the total gain precise.
The asymptotic behaviour of the model comes when A goes towards infinity. Then ξ, β and ν determine the overall gain, when ρ is ignored (which is usually the case).
"Structured Electronic Design" (see references) makes a simplification, which perhaps is not correct. They say that the transfer function of the system is
A_t = \frac{A}{1-A * \beta} + \rho
but that is only true if ξ * ν = 1, in which case At becomes dimensionless. The error they make is ξ and ν cannot be disregarded unless they are dimensionless. They also claim that β is the transfer function of the feedback network. This is usually not the case.
Imagine a voltage amplifier where A is taken as the transconductance of a transistor, and where the gain is set by a voltage divider. Then the dimension of A is conductance (current/voltage), the dimension for β is impedance (voltage/current), whereas the transfer function of the feedback network is dimensionless, and cannot be β.
Resistors
To find the total resistance of all the components, add together the individual resistances of each component:
A diagram of several resistors, connected end to end, with the same amount of current going through each
R_\mathrm{total} = R_1 + R_2 + \cdots + R_n
for components in series, having resistances \ R_1, \ R_2, etc.
To find the current, \ I use Ohm's law I = \frac{V}{R_{total}}
To find the voltage across any particular component with resistance \ R_i, use Ohm's law again. V_i = I \cdot R_i
Where \ I is the current, as calculated above.
Note that the components divide the voltage according to their resistances, so, in the case of two resistors:
\frac{V_1}{V_2} = \frac{R_1}{R_2}
[edit]
Inductors
Inductors follow the same law, in that the total inductance of non-coupled inductors in series is equal to the sum of their individual inductances:
A diagram of several inductors, connected end to end, with the same amount of current going through each
L_\mathrm{total} = L_1 + L_2 + \cdots + L_n
However, in some situations it is difficult to prevent adjacent inductors from influencing each other, as the magnetic field of one device couples with the windings of its neighbours. This influence is defined by the mutual inductance M. For example, if you have two inductors in series, there are two possible equivalent inductances:
\ L_\mathrm{total} = (L_1 + M) + (L_2 + M) or
\ L_\mathrm{total} = (L_1 - M) + (L_2 - M)
Which formula is the correct one, depends how the magnetic fields of both inductors influence each other.
When there are more than two inductors, it gets more complicated, since you have to take into account the mutual inductance of each of them and how each coils influences the other.
So for three coils, there are three mutual inductances (M12,M13 and M23) and eight possible equations.
[edit]
Capacitors
Capacitors follow a different law. The total capacitance of capacitors in series is equal to the reciprocal of the sum of the reciprocals of their individual capacitances:
A diagram of several capacitors, connected end to end, with the same amount of current going through each
{1\over{C_\mathrm{total}}} = {1\over{C_1}} + {1\over{C_2}} + \cdots + {1\over{C_n}}
The working voltage of a series combination of identical capacitors is equal to the sum of voltage ratings of individual capacitors provided that equalizing resistors are used to ensure equal voltage division.
[edit]
Parallel circuits
Voltages across components in parallel with each other are the same in magnitude and they also have identical polarities. Hence, the same voltage variable is used for all circuits elements in such a circuit.
To find the total current, I, use Ohm's Law on each loop, then sum. (See Kirchhoff's circuit laws for an explanation of why this works). Factoring out the voltage (which, again, is the same across parallel components) gives:
I_\mathrm{total} = V \cdot \left(\frac{1} {R_1} + \frac{1} {R_2} + \cdots + \frac{1} {R_n}\right)
[edit]
Notation
The parallel property can be represented in equations by two vertical lines "||" (as in geometry) to simplify equations. For two resistors,
R_\mathrm{total} = R_1 \| R_2 = {R_1 R_2 \over R_1 + R_2}
[edit]
Resistors
To find the total resistance of all the components, add together the individual reciprocal of each resistance of each component, and take the reciprocal of the sum:
A diagram of several resistors, side by side, both leads of each connected to the same wires
{1 \over R_\mathrm{total}} = {1 \over R_{1}} + {1 \over R_{2}} + \cdots + {1 \over R_{n}}
for components in parallel, having resistances R1, R2, etc.
The above rule can be calculated by using Ohm's law for the whole circuit
Rtotal = V / Itotal
and substituting for Itotal
To find the current in any particular component with resistance Ri, use Ohm's law again.
Ii = V / Ri
Note, that the components divide the current according to their reciprocal resistances, so, in the case of two resistors:
I1 / I2 = R2 / R1
[edit]
Inductors
Inductors follow the same law, in that the total inductance of non-coupled inductors in parallel is equal to the reciprocal of the sum of the reciprocals of their individual inductances:
A diagram of several inductors, side by side, both leads of each connected to the same wires
{1\over{L_\mathrm{total}}} = {1\over{L_1}} + {1\over{L_2}} + \cdots + {1\over{L_n}}
Once again, if the inductors are situated in each others' magnetic fields, one has to take into account mutual inductance. If the mutual inductance between two coils in parallel is M then the equivalent inductor is:
{1 \over L_\mathrm{total}} = {1 \over (L_1 + M)} + {1 \over (L_2 + M)} or
{1 \over L_\mathrm{total}} = {1 \over (L_1 - M)} + {1 \over (L_2 - M)}
And once again, which formula is the correct one, depends how the magnetic fields of both inductors influence each other.
The principle is the same for more than two inductors, but you now have to take into account the mutual inductance of each inductor on each other inductor and how they influence each other. So for three coils, there are three mutual inductances (M12,M13 and M23) and eight possible equations.
[edit]
Capacitors
Capacitors follow a different law. The total capacitance of capacitors in parallel is equal to the sum of their individual capacitances:
A diagram of several capacitors, side by side, both leads of each connected to the same wires
C_\mathrm{total} = C_1 + C_2 + \cdots + C_n
The working voltage of a parallel combination of capacitors is always limited by the smallest working voltage of an individual capacitor.
i modified my AGP-slot to an PCI-E
he electromagnetic spectrum is the range of all possible electromagnetic radiation. Also, the "electromagnetic spectrum" (usually just spectrum) of an object is the range of electromagnetic radiation that it emits, reflects, or transmits.
The electromagnetic spectrum, shown in the table, extends from just below the frequencies used for modern radio (at the long-wavelength end) to gamma radiation (at the short-wavelength end), covering wavelengths from thousands of kilometres down to fractions of the size of an atom. It is commonly said that EM waves beyond these limits are uncommon, although this is not actually true. The 22-year sunspot cycle, for instance, produces radiation with a period of 22 years, or a frequency of 1.4*10-9 Hz. At the other extreme, photons of arbitrarily high frequency may be produced by colliding electrons with positrons at appropriate energy. 1024 Hz photons can be produced today with man-made accelerators. In our universe the short wavelength limit is likely to be the Planck length, and the long wavelength limit is the size of the universe itself (see physical cosmology), though in principle the spectrum is infinite.
Electromagnetic energy at a particular wavelength λ (in vacuum) has an associated frequency f and photon energy E. Thus, the electromagnetic spectrum may be expressed equally well in terms of any of these three quantities. They are related according to the equations:
\lambda = \frac{c}f \,\!
and
E=hf \,\!
or
E=hc/\lambda \,\!
where:
* c is the speed of light, 299792458 m/s (c \approx 3 \cdot 10^8 \ \mbox{ m}/\mbox{s} = 300,000 \ \mbox{km}/\mbox{s}).
* h is Planck's constant, (h \approx 6.626069 \cdot 10^{-34} \ \mbox{J} \cdot \mbox{s} \approx 4.13567 \ \mathrm{\mu} \mbox{eV}/\mbox{GHz}).
\hat K_j (1) f(1)= \phi_j(1) \int { \frac{\phi_j^*(2)f(2)}{r_{12}}dv_2}
where \hat K_j (1) is the one-electron Exchange operator,
f(1),f(2) are the one-electron wavefunction being acted upon by the Exchange operator as functions of the positions of electron 1 and electron 2,
φj(1),φj(2) are the one-electron wavefunction of the j-th electron as functions of the positions of electron 1 and electron 2,
r12 is the distance between electrons 1 and 2.
out = νEc + ρEs
Ec = AEi
Ei = βEc + ξEs
The model is maybe called "Black's model".
Here Es is a source quantity and Eout is an output quantity. In electronics, each of Es and Eout can be either a voltage or a current.
Since we are dealing with physical quantities, β * A is dimensionless. ρ has the same dimension as ξ * A * ν.
Now, a feedback amplifier consists of a gain part and a feedback network. The (usually passive) feedback network makes the total gain precise.
The asymptotic behaviour of the model comes when A goes towards infinity. Then ξ, β and ν determine the overall gain, when ρ is ignored (which is usually the case).
"Structured Electronic Design" (see references) makes a simplification, which perhaps is not correct. They say that the transfer function of the system is
A_t = \frac{A}{1-A * \beta} + \rho
but that is only true if ξ * ν = 1, in which case At becomes dimensionless. The error they make is ξ and ν cannot be disregarded unless they are dimensionless. They also claim that β is the transfer function of the feedback network. This is usually not the case.
Imagine a voltage amplifier where A is taken as the transconductance of a transistor, and where the gain is set by a voltage divider. Then the dimension of A is conductance (current/voltage), the dimension for β is impedance (voltage/current), whereas the transfer function of the feedback network is dimensionless, and cannot be β.
Resistors
To find the total resistance of all the components, add together the individual resistances of each component:
A diagram of several resistors, connected end to end, with the same amount of current going through each
R_\mathrm{total} = R_1 + R_2 + \cdots + R_n
for components in series, having resistances \ R_1, \ R_2, etc.
To find the current, \ I use Ohm's law I = \frac{V}{R_{total}}
To find the voltage across any particular component with resistance \ R_i, use Ohm's law again. V_i = I \cdot R_i
Where \ I is the current, as calculated above.
Note that the components divide the voltage according to their resistances, so, in the case of two resistors:
\frac{V_1}{V_2} = \frac{R_1}{R_2}
[edit]
Inductors
Inductors follow the same law, in that the total inductance of non-coupled inductors in series is equal to the sum of their individual inductances:
A diagram of several inductors, connected end to end, with the same amount of current going through each
L_\mathrm{total} = L_1 + L_2 + \cdots + L_n
However, in some situations it is difficult to prevent adjacent inductors from influencing each other, as the magnetic field of one device couples with the windings of its neighbours. This influence is defined by the mutual inductance M. For example, if you have two inductors in series, there are two possible equivalent inductances:
\ L_\mathrm{total} = (L_1 + M) + (L_2 + M) or
\ L_\mathrm{total} = (L_1 - M) + (L_2 - M)
Which formula is the correct one, depends how the magnetic fields of both inductors influence each other.
When there are more than two inductors, it gets more complicated, since you have to take into account the mutual inductance of each of them and how each coils influences the other.
So for three coils, there are three mutual inductances (M12,M13 and M23) and eight possible equations.
[edit]
Capacitors
Capacitors follow a different law. The total capacitance of capacitors in series is equal to the reciprocal of the sum of the reciprocals of their individual capacitances:
A diagram of several capacitors, connected end to end, with the same amount of current going through each
{1\over{C_\mathrm{total}}} = {1\over{C_1}} + {1\over{C_2}} + \cdots + {1\over{C_n}}
The working voltage of a series combination of identical capacitors is equal to the sum of voltage ratings of individual capacitors provided that equalizing resistors are used to ensure equal voltage division.
[edit]
Parallel circuits
Voltages across components in parallel with each other are the same in magnitude and they also have identical polarities. Hence, the same voltage variable is used for all circuits elements in such a circuit.
To find the total current, I, use Ohm's Law on each loop, then sum. (See Kirchhoff's circuit laws for an explanation of why this works). Factoring out the voltage (which, again, is the same across parallel components) gives:
I_\mathrm{total} = V \cdot \left(\frac{1} {R_1} + \frac{1} {R_2} + \cdots + \frac{1} {R_n}\right)
[edit]
Notation
The parallel property can be represented in equations by two vertical lines "||" (as in geometry) to simplify equations. For two resistors,
R_\mathrm{total} = R_1 \| R_2 = {R_1 R_2 \over R_1 + R_2}
[edit]
Resistors
To find the total resistance of all the components, add together the individual reciprocal of each resistance of each component, and take the reciprocal of the sum:
A diagram of several resistors, side by side, both leads of each connected to the same wires
{1 \over R_\mathrm{total}} = {1 \over R_{1}} + {1 \over R_{2}} + \cdots + {1 \over R_{n}}
for components in parallel, having resistances R1, R2, etc.
The above rule can be calculated by using Ohm's law for the whole circuit
Rtotal = V / Itotal
and substituting for Itotal
To find the current in any particular component with resistance Ri, use Ohm's law again.
Ii = V / Ri
Note, that the components divide the current according to their reciprocal resistances, so, in the case of two resistors:
I1 / I2 = R2 / R1
[edit]
Inductors
Inductors follow the same law, in that the total inductance of non-coupled inductors in parallel is equal to the reciprocal of the sum of the reciprocals of their individual inductances:
A diagram of several inductors, side by side, both leads of each connected to the same wires
{1\over{L_\mathrm{total}}} = {1\over{L_1}} + {1\over{L_2}} + \cdots + {1\over{L_n}}
Once again, if the inductors are situated in each others' magnetic fields, one has to take into account mutual inductance. If the mutual inductance between two coils in parallel is M then the equivalent inductor is:
{1 \over L_\mathrm{total}} = {1 \over (L_1 + M)} + {1 \over (L_2 + M)} or
{1 \over L_\mathrm{total}} = {1 \over (L_1 - M)} + {1 \over (L_2 - M)}
And once again, which formula is the correct one, depends how the magnetic fields of both inductors influence each other.
The principle is the same for more than two inductors, but you now have to take into account the mutual inductance of each inductor on each other inductor and how they influence each other. So for three coils, there are three mutual inductances (M12,M13 and M23) and eight possible equations.
[edit]
Capacitors
Capacitors follow a different law. The total capacitance of capacitors in parallel is equal to the sum of their individual capacitances:
A diagram of several capacitors, side by side, both leads of each connected to the same wires
C_\mathrm{total} = C_1 + C_2 + \cdots + C_n
The working voltage of a parallel combination of capacitors is always limited by the smallest working voltage of an individual capacitor.
Last edited by ']['error (2006-09-12 10:15:13)