Embedded Microcomputer Systems Lecture 9.1 by Jonathan W. Valvano Recap from last time • Analog circuit design • Noise • Microphone interface Objectives • Active low pass filter • Nyquist Theorem and aliasing • Speaker amplifier Looking at noise, observe system with known input Magnitude Type 1) DVM AC mode => good for quantitative level 2) Scope Peak-peak => rough measure of quantitative level Shape => type of noise 3) Spectrum analyzer Signal to noise ratio TypeEmbedded Microcomputer Systems Lecture 9.2 by Jonathan W. Valvano dbFS = 20log10(V/1.5) Filter types Analog LPF BPF HPF Digital Extremely flexible Butterworth Filters 2 pole Butterworth analog filter 1) select the cutoff frequency, fc 2) divide the two capacitors by 2πfc (let C1A, C2A be the new capacitor values) C1A = 141.4μF/2πfc C2A = 70.7μF/2πfc 3) locate two standard value capacitors (with the 2/1 ratio) with the same order of magnitude as the desired values let C1B, C2B be these standard value capacitors, let x be this factor C1B = C1A/x C2B = C2A/x 4) adjust the resistors to maintain the cutoff frequency R = 10kΩ•x )RRinVVoutinV=fc11 +f4(C1141.4µF10kΩ10kΩC270.7µFoutV Two pole Butterworth low pass analog filter. Capacitor specification low leakage (impedance), accuracy (tolerance) low temperature coefficient temperature range, voltage range, frequency range, Extremely High Quality Capacitors Teflon, polystyrene Polypropylene, 1,2,3,5%. Medium Quality Capacitors 5%, 10%, 20% tolerance Class 1, C0G ceramic, 5%, 30ppm/oC, ±0.3% over -55 to 125 oC Class 2, X7R ceramic, 10%, ±15% over -55 to 125 oC Class 3, Z5U ceramic, 20%, 22 to -56% over 10 to 86 oC Performance Tip: If you choose standard value resistors near the desired values, you will save money and the circuit will still be a Butterworth filter. The only difference is that the cutoff frequency will be slightly off from the original specification. ***********Show LPF.XLS**************** Show TI FilterProEmbedded Microcomputer Systems Lecture 9.3 by Jonathan W. Valvano General Instrumentation/Control SystemMeasurandTransducer Calibration SignalElectromagnetic Electrical Thermal Sound OpticalAnalog PreampAnalog Filter and AmplificationMicrocomputerADC Primary sensing Variable conversionReal worldtimerx(t) y(t)z(t)Actuator applies energy Quantitative DAS (thermometer in EE445L) range (rx) resolution (Δx) precision (nx in alternatives) frequencies of interest (fmin to fmax) Qualitative DAS (sound recording in EE345M) “sounds good” “looks pretty” “feels right” Other qualitative DAS’s involve the detection of events. true positive (TP) baby stops breathing and apnea monitor detects it false positive (FP) baby is breathing OK but apnea monitor alarms false negative (FN) baby stops breathing but monitor does not alarm Prevalence = (TP + FN) / (TP + TN + FP + FN) Sensitivity = TP / (TP + FN) Specificity = TN / (TN + FP) PPV = TP / (TP + FP) NPV = TN / (TN + FN) Using Nyquist Theory to Determine Sampling Rate. Voltage quantizing precision nz = 2n Time quantizing Time (s)048121620242832012345678910Continuous analog signalDiscrete digital signalEmbedded Microcomputer Systems Lecture 9.4 by Jonathan W. Valvano Nyquist theory states that if the signal is sampled at fs, then the digital samples only contain frequency components from 0 to ½fs. Conversely, if the analog signal does contain frequency components larger than ½fs, then there will be an aliasing error. Aliasing is when the digital signal appears to have a different frequency than the original analog signal. ***********Show FFT16.XLS**************** The choice of sampling rate, fs, is determined by the maximum useful frequency contained in the signal. fs > 2 fmax A low pass analog filter may be required to remove frequency components above 0.5fs. A digital filter can not be used to remove aliasing. Analog Filter Let the gain of the analog filter be G3 = ⎢H3(s)⎢. Then the system should pass, with little error as seen by the ADC, for signal frequencies between fmin and fmax. 22 + 1nnn22 - 1n0.70700fcfminfcfmax0.5 fsIdealG3Frequency1Filter with no A/D error aliasedproperly representedundetectablefrequencyZ2Δzfs1 2 Ideal and practical filter responses. To prevent aliasing => no measurable signal above 0.5fs. Speaker interface 20kΩ0.1μF10kΩ1μFMC341194.7μF324V-V+FCCD15867+5VVccVO1VO2GndR10R11C5CSSClkDin Gnd+3.3VOutFBncSSI0MAX5353SSI0FssSSI0ClkSSI0TxSSI0Rx10 kΩ3.3 V5.1 kΩ+1.233VLM4041CILP10 kΩVdd4.7 μF0.1 μFREF EE445Lbook, figure 10.36 Need an audio amp to connect DAC output to 32Ω speaker Be careful to limit voltage and power to speakerEmbedded Microcomputer Systems Lecture 9.5 by Jonathan W. Valvano 0 < V < 5V P < 200 mW 0.2 W > (VO1-VO2)2/32Ω (VO1-VO2) < 2.5V 0.2 W > (VO1-VO2)2/8Ω (VO1-VO2) < 1.2V Look up maximum current for your board Measure it with an external +5V supply and a current meter Choose Rf, Ri so 2*Rf/Ri is less than 1 Mount the speaker in a box http://www.lalena.com/Audio/FAQ/Speaker/ Design choices ADC bits Sampling rate Cheaper cables and electronics cause more noise Analog filters Cheaper microphone and speakers introduce more noise Refer errors to the system specification Quantitative system errors cause inaccuracy Qualitative system errors cause it to sound