User:John R. Brews/Images

Angle brackets: & #x27E8; = ⟨   & #x27E9; = ⟩   & #10216; = ⟨   & #10217;= ⟩ <Φ|Ψ> <Φ|Ψ> <Φ|Ψ> ⟨Φ|Ψ⟩ ⟨Φ|Ψ⟩ $\langle \Phi |\Psi \rangle$ ⟨Φ|Ψ⟩ ⟨Φ|Ψ⟩

Photos

Photos

(PD) Photo: John R. Brews Mourning dove on nest in Tucson     (PD) Photo: John R. Brews Morning dove with squab, Tucson AZ.     (PD) Photo: John R. Brews Mourning dove with squab.     (PD) Photo: John R. Brews Mourning dove squab.     (PD) Image: John R. Brews Mourning dove on saguaro cactus, Tucson AZ.

Magnetism

Magnetism

(CC) Image: John R. Brews B-field lines near uniformly magnetized sphere     (CC) Image: John R. Brews Magnetic flux density vs. magnetic field in steel and iron     (PD) Image: John R. Brews B-field from current I2 in wire 2 causes force F on wire 1.

Chemistry

Chemistry

(PD) Image: John R. Brews Reactants cross an energy barrier, enter an intermediate state and finally emerge in a lower energy configuration.

Circuits

Current sources

(CC) Image: John R. Brews Widlar current source using bipolar transistors     (CC) Image: John R. Brews Small-signal circuit for finding output resistance of the Widlar source     (CC) Image: John R. Brews Design trade-off between output resistance and output current in Widlar source     (PD) Image: John R. Brews A current mirror implemented with npn bipolar transistors using a resistor to set the reference current IREF; VCC = supply voltage.     (PD) Image: John R. Brews An n-channel MOSFET current mirror with a resistor to set the reference current     (PD) Image: John R. Brews Gain-boosted current mirror with op amp feedback to increase output resistance.     (PD) Image: John R. Brews MOSFET version of wide-swing current mirror; M1 and M2 are in active mode     (PD) Image: John R. Brews Operational-amplifier based current sink. Because the op amp is modeled as a nullor, op amp input variables are zero regardless of the values for its output variables.     (PD) Image: John R. Brews A digital inverter circuit using a bipolar transistor.     (PD) Image: John R. Brews Transfer characteristic of bipolar inverter showing modes.     Collector current vs. input voltage for a bipolar inverter with VCC=5V and RC=1kΩ.     (PD) Image: John R. Brews Input and output signals for bipolar inverter used as an amplifier.     (PD) Image: John R. Brews Two-port network with symbol definitions.     (PD) Image: John R. Brews Z-equivalent two port showing independent variables I1 and I2.     (PD) Image: John R. Brews Y-equivalent two port showing independent variables     (PD) Image: John R. Brews H-equivalent two-port showing independent variables     (PD) Image: John R. Brews G-equivalent two-port showing independent variables     (PD) Image: John R. Brews Block diagram for asymptotic gain model     (PD) Image: John R. Brews Possible signal-flow graph for the asymptotic gain model     (PD) Image: John R. Brews MOSFET transresistance feedback amplifier.     (PD) Image: John R. Brews Collector-to-base biased bipolar amplifier.     (PD) Image: John R. Brews Two-transistor feedback amplifier; any source impedance RS is lumped in with the base resistor RB.

Small-signal circuits

(PD) Image: John R. Brews Small-signal circuit for pn-diode driven by a current signal represented as a Norton source.     (PD) Image: John R. Brews Bipolar current mirror with emitter resistors     (PD) Image: John R. Brews Small-signal circuit for bipolar current mirror     (PD) Image: John R. Brews Common base circuit with active load and current drive.     (PD) Image: John R. Brews Common-base amplifier with AC current source I1 as signal input     (PD) Image: John R. Brews Bipolar transistor with base grounded and signal applied to emitter.     (PD) Image: John R. Brews Common-base amplifier with AC voltage source V1 as signal input     (PD) Image: John R. Brews The result of applying Norton's theorem.     (PD) Image: John R. Brews Bipolar current buffer.     (PD) Image: John R. Brews Small-signal circuit to find output current.     (PD) Image: John R. Brews Small-signal circuit with test current iX to find Norton resistance.     (PD) Image: John R. Brews The result of applying Thévenin's theorem.     (PD) Image: John R. Brews Bipolar buffer.     (PD) Image: John R, Brews Small-signal circuit for voltage follower.     (PD) Image: John R. Brews Determination of the small-signal output resistance.     (PD) Image: John R. Brews Simplified, low-frequency hybrid-pi BJT model.     (PD) Image: John R. Brews Bipolar hybrid-pi model with parasitic capacitances.     (PD) Image: John R. Brews Simplified, low-frequency hybrid-pi BJT model.     (PD) Image: John R. Brews Bipolar hybrid-pi model with parasitic capacitances.     (PD) Image: John R. Brews Simplified, three-terminal MOSFET hybrid-pi model.     (PD) Image: John R. Brews Four-terminal small-signal MOSFET circuit.     (PD) Image: John R. Brews Miller effect: These two circuits are equivalent.     (PD) Image: John R. Brews Small-signal circuit for transresistance amplifier     (PD) Image: John R. Brews Small-signal circuit with return path broken and test current it driving amplifier at the break.     (PD) Image: John R. Brews Three small-signal schematics used to discuss the asymptotic gain model

Return ratio

(PD) Image: John R. Brews Left - small-signal circuit corresponding to bipolar amplifier; Center - inserting independent source and marking leads to be cut; Right - cutting the dependent source free and short-circuiting broken leads.

Amplifiers

(PD) Image: John R. Brews Some terms used to describe step response in time domain.     (PD) Image: John R. Brews Ideal negative feedback model; open loop gain is AOL and feedback factor is β.     (PD) Image: John R. Brews Conjugate pole locations for step response of two-pole feedback amplifier.     (PD) Image: John R. Brews Step-response of a linear two-pole feedback amplifier.     (PD) Image: John R. Brews Step response for three values of time constant ratio.     (PD) Image: John R. Brews Bode gain plot to find phase margin of two-pole amplifier.     (PD) Image: John R. Brews The Bode plot for a first-order (one-pole) highpass filter     (PD) Image: John R. Brews The Bode plot for a first-order (one-pole) lowpass filter     (PD) Image: John R. Brews Bode magnitude plot for zero and for low-pass pole     (PD) Image: John R. Brews Bode phase plot for zero and for low-pass pole     (PD) Image: John R. Brews Bode magnitude plot for pole-zero combination; the location of the zero is ten times higher than in above figures     (PD) Image: John R. Brews Bode phase plot for pole-zero combination; the location of the zero is ten times higher than in above figures     (PD) Image: John R. Brews Gain of feedback amplifier AFB in dB and corresponding open-loop amplifier AOL.     (PD) Image: John R. Brews Phase of feedback amplifier °AFB in degrees and corresponding open-loop amplifier °AOL.     (PD) Image: John R. Brews Gain of feedback amplifier AFB in dB and corresponding open-loop amplifier AOL.     (PD) Image: John R. Brews Phase of feedback amplifier AFB in degrees and corresponding open-loop amplifier AOL.     (PD) Image: John R. Brews Operational amplifier with compensation capacitor CC between input and output to cause pole splitting.     (PD) Image: John R. Brews Operational amplifier with compensation capacitor transformed using Miller's theorem to replace the compensation capacitor with a Miller capacitor at the input and a frequency-dependent current source at the output.     (PD) Image: John R. Brews Idealized Bode plot for a two pole amplifier design.     (PD) Image: John R. Brews Miller capacitance at low frequencies CM (top) and compensation capacitor CC (bottom) as a function of gain

Math

Math & logic

(PD) Image: John R. Brews Venn diagrams; set A is the interior of the blue circle (left), set B is the interior of the red circle (right).     (PD) Image: John R. Brews Venn diagrams; set X is the interior of the blue circle (left), set Y is the interior of the red circle (right).     (PD) Image: John R. Brews Venn diagram showing subsets of two sets X and Y.     (PD) Image: John R. Brews Venn diagram for three sets X, Y, and Z.     (PD) Image: John R. Brews Venn diagram for four sets X, Y, Z, and W.     (PD) Image: John R. Brews Venn diagram for five sets X, Y, Z, V and W.     (PD) Image: John R. Brews A three-input logic gate (center) with its Venn diagram (top) and truth table (bottom).     (PD) Image: John R. Brews Five-switch network with Venn diagrams for branches     (PD) Image: John R. Brews Equivalent three-switch network with Venn diagrams for branches

Forces

Forces

(CC) Image: John R. Brews Force and its equivalent force and couple     (PD) Image: John R. Brews Centripetal force FC upon an object held in circular motion by a string of length R. The string is under tension FT, as shown separately to the left.     (PD) Image: John R. Brews Upper panel: Ball on a banked circular track moving with constant speed v; Lower panel: Forces on the ball.     (PD) Image: John R. Brews Polar unit vectors at two times t and t + dt for a particle with trajectory r ( t ); on the left the unit vectors uρ and uθ at the two times are moved so their tails all meet, and are shown to trace an arc of a unit radius circle.     (PD) Image: John R. Brews Local coordinate system for planar motion on a curve.     (PD) Image: John R. Brews Exploded view of rotating spheres in an inertial frame of reference showing the centripetal forces on the spheres provided by the tension in a rope tying them together.     (PD) Image: John R. Brews Rotating spheres subject to centrifugal (outward) force in a co-rotating frame in addition to the (inward) tension from the rope.     (PD) Image: John R. Brews The "whirling table". The rod is made to rotate about the axis and (from the bead's viewpoint) the centrifugal force acting on the sliding bead is balanced by the weight attached by a cord over two pulleys.     (PD) Image: John R. Brews Force diagram for an element of water surface in co-rotating frame.     (PD) Image: John R. Brews An object located at xA in inertial frame A is located at location xB in accelerating frame B.     (PD) Image: John R. Brews An orbiting but fixed orientation coordinate system B, shown at three different times.     (PD) Image: John R. Brews An orbiting coordinate system B in which unit vectors uj, j = 1, 2, 3 rotate to face the rotational axis.     Crossing a rotating carousel walking at constant speed, a spiral is traced out in the inertial frame, while a simple straight radial path is seen in the frame of the carousel.     (PD) Image: John R. Brews Rotating shaft unbalanced by two identical attached weights. Image     (PD) Image: John R. Brews Torque vector T representing a force couple.     (PD) Image: John R. Brews An ellipsoid showing its axes     While the pendulum P swings in a fixed plane about its hanger at H, the planes of the Earth observer rotate.     As time progresses each unit vector's change is orthogonal to it.     Tossed ball on carousel. At the center of the carousel, the path is a straight line for a stationary observer, and is an arc for a rotating observer.     From the center of curvature of the path, the ball executes approximate circular motion.     Some useful notation for the ball toss on a carousel.     The ball follows a nearly circular path about the center of curvature.     The inertial forces on the ball combine to provide the resultant centripetal force required by Newton's laws for circular motion.     Stats for a particular path of ball toss.     Tangent-plane coordinate system on rotating Earth at latitude φ.     Wind motion in direction of pressure gradient is deflected by the Coriolis force.     In the northern hemisphere, Coriolis force forms a counterclockwise flow.     Path of ball for four rates of rotation. Catcher positioned so the catch is made at 12 o'clock in all cases.     A fluid forced through a rocking tube experiences a Coriolis acceleration.

Electromagnetism

Electromagnetism

Electric motor using a current loop in a magnetic flux density, labeled B     The Fizeau apparatus for measuring the speed of light by passing it between the cogs of a rotating gear and reflecting it back through adjacent cogs.     Measuring a length using interference fringes.     The wavelengths of standing waves in a box that have zero amplitude (nodes) at the walls.     Measuring a length in wavelengths of light using a Michelson interferometer.     Boat opposing incoming waves experiences the Doppler effect     Doppler shift with moving source     Infinitesimal current elements in two closed current-carrying loops     Origin at 0, observation point at P, and present position of charge q distant by R from observation point P.

Devices

Devices

Mesa diode structure (top) and planar diode structure with guard-ring (bottom).     A planar bipolar junction transistor as might be constructed in a integrated circuit.     Gummel plot and current gain for a GaAs/AlGaAs heterostructure bipolar transistor.     Quasi-Fermi levels and carrier densities in forward biased pn-diode.     Cross section of MOS capacitor showing charge layers     Three types of MOS capacitance vs. voltage curves. VTH = threshold, VFB = flatbands      Small-signal equivalent circuit of the MOS capacitor in inversion with a single trap level     A modern MOSFET     A power MOSFET; source and body share a contact.     Two bipolar transistor modes, showing extrapolation of asymptotes to the Early voltage.     Channel length modulation in 3/4μm technology.     Early voltage for MOSFETs from a 0.18μm process as a function of channel strength.     Calculated density of states for crystalline silicon.     Field effect: At a gate voltage above threshold a surface inversion layer of electrons forms at a semiconductor surface.     Occupancy comparison between n-type, intrinsic and p-type semiconductors.     Nonideal pn-diode current-voltage characteristics     Band-bending diagram for pn-junction diode at zero applied voltage     Band-bending for pn-diode in reverse bias     Quasi-Fermi levels in reverse-biased pn-junction diode     Band-bending diagram for pn-diode in forward bias     Fermi occupancy function vs. energy departure from Fermi level in volts for three temperatures     Fermi surface in k-space for a nearly filled band in the face-centered cubic lattice     A constant energy surface in the silicon conduction band consists of six ellipsoids.     Planar Schottky diode with n+-guard rings and tapered oxide.     Comparison of Schottky and pn-diode current voltage curves.     Schottky barrier formation on p-type semiconductor. Energies are in eV.     Schottky diode under forward bias VF.     Schottky diode under reverse bias VR.     Critical electric field for breakdown versus bandgap energy in several materials.     Schottky barrier height vs. metal electronegativity for some selected metals on n-type silicon.

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Vestibular system

Vestibular system

When the semicircular canal stops rotating, inertia causes the cupula to register a false rotation in the opposite sense.     Top: The semicircular canals with head erect. Bottom: the canals with head tipped forward.