Slide 1'&$%ECE/CE 3720: Embedded System DesignChris J. MyersLecture 23: DAS DesignSlide 2'&$%Block Diagram1Slide 3'&$%Sampling Rate, fs, Less than 2 fmaxSlide 4'&$%Sampling Rate, fs, Equals 2 fmax2Slide 5'&$%Sampling Rate, fs, Greater than 2 fmaxSlide 6'&$%Fixed Sampling Rate3Slide 7'&$%Fixed Sampling RateSlide 8'&$%How Many Bits Does One Need for the ADC?• If transducer is nonlinear, then ADC precision must belarger than the precision specified in the problem.y = f(x)∆x=rxnx∆y= min{f(x + ∆x) − f(x)} for all x in rxny=ry∆y• Example: 0 ≤ x ≤ 1 with desired resolution ∆x= 0.01.4Slide 9'&$%Specifications for the Analog Signal ProcessingSlide 10'&$%Impedance Loading5Slide 11'&$%Impedance Loading Problem and SolutionSlide 12'&$%How Fast Must the ADC Be?• ADC conversion time must be smaller than quotient ofsampling interval by number of multiplexor signals.• If fsis sampling frequency, m is number of multiplexorsignals, tmuxis settling time of the multiplexer, and tcisADC conversion time, then without S/H:m · (tmux+ tc) < 1/fs• With S/H, must include aquisition time, taq, andaperture time, tap:m · (tmux+ taq+ tap+ tc) < 1/fs6Slide 13'&$%Specifications for the S/H• A S/H is required if the analog input changes more thanone resolution during the conversion time.• A S/H is required if:dzdt· tc> 0.5∆zwhere dz/dt is maximum slope of ADC input voltage, ∆zis the ADC resolution, and tcis the ADC conversion time.Slide 14'&$%Synchronized Sampling7Slide 15'&$%Analysis of Noise• Any system will fail if signal is overwhelmed by noise.• Fundamental noise (i.e., cannot be removed):1. Thermal noise (or white noise)2. Shot noise3. 1/f noise4. Transducer limitations• Added noise includes many disturbing external factors:1. Magnetic induction2. Displacement currents, or capacitive coupling3. Impedance loading4. Common mode rejection ratio (CMRR)5. Frequency response6. Motion artifactSlide 16'&$%Thermal Noise1Hz 10Hz 100Hz 1kHz 10kHz 100kHz 1MHz10 kΩ 14nV 45nV 142nV 448nV 1.4µV 4.5µV 14µV100 kΩ 45nV 142nV 448nV 1.4µV 4.5µV 14µV 45µV1 MΩ 142nV 448nV 1.4µV 4.5µV 14µV 45µV 145µV8Slide 17'&$%Root Mean Square (RMS)Percent of time peak is exceeded Crest factor (peak/RMS)1.0 2.60.1 3.30.01 3.90.001 4.40.0001 4.9Slide 18'&$%Thermal Noise: Example AnalysisWithout C With CVJ14.5µV 142nVVJ245µV 1.4µVq[(100Vj1)2+ (Vj2)2] 452µV 14.3µV9Slide 19'&$%Shot Noise• Arises from statistical uncertainty when counting events.• For example, thermal cameras count individual photons.n = dn/dt∆twhere dn/dt is the count rate, and ∆t is the count time.• The shot noise is:Shot noise =qdn/dt∆t• The S/N ratio is:S/N =n√n=qdn/dt∆t• Tradeoff between accuracy and measurement time.Slide 20'&$%1/f or Pink Noise• Present in devices with connections between conductors,and results from fluctuating conductivity.• Important for low-bandwidth applications.• Wire-wound resistors do not have 1/f noise, butsemiconductors do.• 1/f noise for a carbon resistor:Vc= (10−6)q1/fRIp∆γf(Hz) Vc(µV )1 31610 100100 321000 1010Slide 21'&$%Transducer Limitations• Certain transducers have intrinsic limitations due to theirdesign or construction.• For example, wire-wound potentiometer as a positiontransducer is limited by the number of wire turns.Slide 22'&$%Magnetic Field Induction• Magnetic fields can induce a voltage.• One of two sources of 60 Hz noise.• Changing magnetic field must pass through a wire loop.• Noise is proportional to strength of magnetic field, B,area of the loop, S, and geometric factor, K.11Slide 23'&$%Displacement Currents or Capacitive CouplingSlide 24'&$%Impedance Loading12Slide 25'&$%Common Mode Rejection Ratio (CMRR)Slide 26'&$%Frequency Response and Motion Artifact• All instrumentation systems are band-limited.• As frequency increases, gain decreases.• Gain error usually affects the instrument objective.• Motion can introduce errors in many ways.• Moving cables can induce currents, change connectorimpedance, or disconnect.• Acceleration of the transducer often affects its response.13Slide 27'&$%Temperature Measurement System• Range of T is 0 to 50◦C with resolution of 0.25◦C, and afrequency range of 0 to 0.1Hz.• Transducer has slope of 10◦C/s and resistance:R = 100 + 0.4TSlide 28'&$%Temperature Measurement System• Needed ADC precision is 50◦C/0.25◦C = 200, so 8-bits.• Use bridge circuit to convert RTD resistance into voltage.• ADC range 0 to 5V and V1− V2is 0 to 0.0191V, so ampneeds gain of 261.• If ADC conversion time is 25µs, no S/H needed because:10◦C/s · 25µs = 0.00025◦C << 0.25◦C• Noise must be less than the resolution (75µV).Amplifier noise ≤resolution2= 37µV14Slide 29'&$%Temperature Measurement System• One-pole low-pass analog filter needed to pass signal from0 to 0.1Hz, reject noise >0.1Hz, and prevent aliasing.• To prevent aliasing, Z2must be less than ADC resolutionfor all frequencies larger than or equal to 0.5fs.• Effective output impedence is 100Ω. Input impedance ofamp must high enough not to affect ADC (>51.2 kΩ).Slide 30'&$%Amplifier and Low-Pass FilterT (◦C) RTD(Ω) V1V2V1− V2V3= V4ADC output0.0 100.0 0.0980 0.0980 0.0000 0.0 0000,00000.25 100.1 0.0981 0.0980 0.0001 0.025 0000,000125.0 110.0 0.1076 0.0980 0.0096 2.500 1000,000050.0 120.0 0.1172 0.0980 0.0191 5.000 1111,111115Slide 31'&$%Force Measurement Systemx(N) y(mV) z(V)Minimum -1 -100 -10Zero 0 0 0Resolution 0.001 0.1 0.01Maximum 1 100 10Range 2 200 20Precision 2000 2000 2000Slide 32'&$%Amplifier and Filter16Slide 33'&$%Thermocouple InterfaceSlide 34'&$%Thermocouple InterfaceT2(◦C) Rt(Ω) Reqv(Ω) Vb(mV )20 1964 719.7 1.0422 1703 681.5 1.1424 1480 642.8 1.2526 1289 603.8 1.3528 1124 565.1 1.4630 982.5 526.9 1.4617Slide 35'&$%Heart SoundsSlide 36'&$%Heart Sound Measuring System18Slide 37'&$%Position Measurement