chapter 5 lecture 10 spring 2015. nonlinear elements 1. a nonlinear resistance 2. a nonlinear...
TRANSCRIPT
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Chapter 5 Lecture 10
Spring 2015
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Nonlinear Elements
• 1. A nonlinear resistance • 2. A nonlinear reactance• 3. A time varying element in you circuit or
system. • 4. These elements show up in many form and
the biological ones are more complicated than the electronic ones.
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Basic Characteristic of NonlinearDevices.
• 1. Nonlinear resistance,
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An Ideal Harmonic Generator
• 1 The simple one is a diode. I= Vo+αV1+βV2+----
• V
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Test Circuit
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Results
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Nonlinear Reactance
• 1. Use to convert power from one frequency to another.
• 2 Typical diode C~(V)-1/2 for step diode• 3 How do you design a diode with a larger
nonlinear capacitance?• P-_ N_ P+ N+ Ni N+
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Parametric Amplifiers
• 1. Conservation of Energy on a photon basis
• 2. Conservation of momentum where k is the propagation constants
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Parametric Amplifiers
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Biological Amplifiers
• http://www.unmc.edu/physiology/Mann/mann13.html
• Neural Transmitter Releases up to 104 calcium ions• Need to overcome the electrical threshold for firing
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Stochastic Resonance
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Stochastic Resonance
12
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Nonlinear Effects at Cell Membranes
1. Current flow for
2. Rm is the membrane resistance. The result is that the membrane is a poor rectifier. However AC voltages make the interior more negative.
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AC Induced Current Flows At Low Frequencies
Induced DC Currents for VAC from -60 to + 40mV
For a spherical cell.
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Shift in Membrane Firing Time
• Shift in firing time for• Where u(t) is unit step function
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Mode Locking of Oscillators
• Theory for injection locking of electronic oscillators is give by
• The theory is good for case where
• This worked for Aplysia pacemaker cells.
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Threshold Injection Lockingfor an Aplysia Pacemaker Cell
• Frequency range from 2 to 10 Hz
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Signal Noise Requirements for Phase Locking
• The phase of the inject signal must be stable enough so that the phase φ
• Where K is the linear control characteristic in units (2π Hz/V) and is closely related to the loop gain.
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Locking of a Pacemaker Cell
• Response to various frequencies of injected currents.
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Signal Coherence
• Litovitz showed that for 10µT coherence for 10 seconds or longer was required for signals at 55 or 65 Hz was required to change the activity of
• τcell= 8 sec
sec8cell
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Litovitz shows both space and time coherence help separate signals from Noise
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Results Show
• 1. Both Space and time Coherence are important.
• 2 Small electric fields can lead to biological changes.
• 3. Magnetic fields can affect biological changes by a separate mechanism.
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Effects of Time Delay Between E and J
• This can give Z in all four quadrants.
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Membrane Capacity as a Function of Frequency
• Membrane Capacity is only a small function of voltage.
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Repetitive Stimulation
• 1. Repetitive microwave pulse resulted in decreasing the amount of slowing for a pacemaker cell in Aplysia.
• 2. Repetitive electrical stimulation lead to decreases in the resistance of gap junctions and to a 62% increase in coupling between cells.
• 3. These are likely to be the result of feedback leading to adaptive responses.
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A Neural Network Model for Adaptive Responses
• 1
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Training to Recognize 60Hz as a Function of S/N with 97% Accuracy
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Thermal Calculations
• Power in and rate of change of temperature
Maximum Temperature change for a small sphere with total energy in H
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Thermal Chemistry • S = fraction that under gone chemical change• K’ is the chemical reaction rate. • R’ is the gas constant• H’ is free energy , S’ is the entropy.
• This leads to an exponential of an exponential
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Thermal Chemistry
• 1. Rule of thumb we are likely to see biological changes when
• 2. The body typically holds your temperature to +/- 0.5oC
• 3. Very rapid changes in chemical reaction rates above a threshold. !!
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The Rate of Change of Temperature is also Important.
• 1 We have shown the changes of 1/10 oC can change the firing rate of a pacemaker cell at 1oC/sec.
• From the Nernst Equation
• Slow increases in T increased firing rates of a pacemaker cell rapid one decreased it. Changes seen with as little as 0.1 o C at rates of 1o C/sec
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Effects of Rapid Heating
• Picture from • Aplysia
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Discussion
• 1. It takes high powers and short pulses to get significant temperature differences on small objects.
• 2. Thin films have larger surface to volume ratios and cool faster than spheres .
• 3. Blood flow cools hot spots. • 4. The thermal time constant is an important
parameter and the sensitive to temperature change is one of the first measurements to make on any experiments involving RF or Microwaves.
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Discussion
• 1. Temperature pulses lead to thermal expansion and can cause acoustic waves that can be sensed at a distance.
• 2. Example radar hearing.
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Natural and Man-Made Fields
• 1. The atmosphere charged about 100/sec world wide with about an 18 sec time constant to about 130V/m
• 2. Peak values at about 3000V/m• 3. Rapid decrease with frequency to typical
value > 1 Hz of 10-4 V/m• 4. These numbers are all variable
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Internal Fields
• 1. Across a membrane of 2 x 107V/m• 2. Nerve pulses about 0.4ms , rise time 0.1ms
fall time 0.5ms. Dead space 1 to 3ms• 3. Fields along the outside of a nerve cell • 5x10-2V/m• 4. These numbers are variable with position,
type of cell etc.
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Types of Noise
• 1. Thermal • 2. Shot Noise • 3. C/fn Noise• 4. Noise generated by other electrical activity
in the Body.
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Thermal Noise.
• 1. Pn= kTB = kTΔf• 2. Other forms for matched loads
• 3 For thermal equilibrium. Non-equilibrium get negative temperatures.
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Spontaneous Emission and Shot Noise
• 1 Spontaneous Emission • P= hfΔf • 2. Shot Noise
• 3. 1/f Noise or
• Where S(f) is the power spectral density
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Example
• 1. For mylar film
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Membrane Example.• 1
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Other Electrical Activity
• 1. EEG• 2. ECG or EKG• 3 Muscle movement.• 4. Nerve Cells Firing
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Minimum Detectable Electric FieldIs a Function of Frequency
• Bovine Fibroblast• Cells
I= 10-3—10A/m2