Question

Analysis and Design of Low Pass Filters 1 of 3 > Before designing the throne must understand the relationship between the output voltage of the circut and the frequency. For a series RL crout, how do the impedances of the circut elements depend on the frequency? Select the correct answer View Available Hintſ Learning Goal: To analyze and design a passive, first-order low-pass filter using a series RL rout. The analysis and design will be repeated for a series RC Croit An electrocardiogram needs to detect periodio signals of Approximately 1 Ita since the resting heart rate of a healthy adult is between 55 od 70 beats per minute). The instrument operates in an electrical environment that is very noisy with a frequency of 60 He is desirable to have a low-pass filter that will block any noise above 18 H A low pasa RE liter can be built using available 130 Hinductors a low pass RC Mercan be built using available 32 F capuchons, resistors of any necessary value are also available The magritude of the impedance of the resistor is independent of the frequency, the magnitude of the impedance of the inductor increases when the frequency increases The magnitude of the impedance of the resistor increases when the frequency increases the magnitude of the impedance of the inductor decreases when the frequency increases Both impedance magnitudes are independent of the frequency The magnitude of the impedance of the resistoria independent of the frequency, the magnitude of the impedance of the inductor decreases when the frequency increases The magnitude of the impedance of the resistor increases when the frequency increases the magnitude of the impedance of the inductor is ependent of the frequency Submit - Part B. Designing and analyzing a series Allow-pass filer Using the walle 130 Hinductor, what is the value of the rest needed to make a low-pass filter with a cutofrequency of 18 H? Express your answer to three significant figures and include appropriate units. View Available in HA ? R- Value Units Submit

Answer 1

Soln:- Series RL low pass filter L R Vout Nih XL = 271 FL Xi af X,Å Whent Thus first option is carrect The magnitude of the resistor is independek of frequency, the magnitude of the impedance of the inductor increases when frequency increases. Part B Cut off frequency Z R 2TL 18 = R 277 X130 or, R = 27TX 130X18 14702.65 s z 14.7km

Parta Vin= 1 v Vin Output voltage Vout = R Rtjul Vout (1H2) = | R R+j271 277 X 1X13 3o * R X) R+ 4T?x12x1301? X 1 14902.65 V 14702.65% + 4T 'x 1302 = 0.998 v 1 470 2,65 6 | Vaut 12 He) = 14702.65'+ 47 4X182x1302 Vout = 0,707 v

Nout(60 Hz)) = 14 T02-65 1470 2,653+ 4TT X 602X1302 - 0.287V Part D: series RC Low pass filter R mw + T Vout Vin "Т 1. 1 Xc L » Xct whenfa XC- Zafc f Second option is correct The impedance of resistor is independent the impedance of capacitor decreases when frequency increases. Parte : Cut off frequency: 18 Hz Given C = 3.20F of frequency,

foz 1 2TRC or 187 1 2T RX3.2x106 or Ro ܥܙ 27T X3.2x10-6 X 18 = 2763.1 r - 2 2.763 kr Part Fi Output voltage, Input voltage 1 Vout= Vinx Xc Vin R²+Xc ( "/2006) √ R²+ (17) ² Vout L1H2) ܥܢ N 27 X1 X 3.2x10-6 2163.1² + ܥܢ 2 2 TTXIX 3.2x106

ori Hout ( 1 Hz)0.998 v | Vout (18H2) ܝܙ (271X18X 3.2X106) 1 2763.12 + 21TX 18 X 3.2x10-6 - 0.707 V Hout (60 H2) = 0.287 V