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How to convert PDF to Word programmatically in C# using PDF Focus . Net assembly.

(95)

Let (sL , sR ) denote the arc length traveled by the left and right wheels, respectively Due to the no slip assumption and assuming that sL (0) = sR (0) = L (0) = R (0) = 0, we have the conditions L = 1 sL sL = RL L RL (96) sR = RR R R = 1 sR

Again, add the values: jX = j30 + ( j110) = j(30 110) = j80 This is a pure capacitive reactance, because it is negative imaginary

where the angular rotation of the left and right axles ( L , R ) are de ned in eqn (91) By the de nition of arc length, we have sL = uL sR = u R (97)

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Problem 16-3 Suppose a coil of inductance L = 500 H and a capacitor of capacitance C = 200 pF are connected in series Suppose the frequency is f = 400 MHz What is the net reactance First, calculate the reactance of the inductor at 400 MHz Proceed as follows:

Therefore, by substituting eqn (97) into the derivative of eqn (96) and solving for (uL , uR ) we obtain uL = RL L u R = RR R Finally, combining eqns (91), (93), (95) and (98) we obtain n = 1 2 (RL eL + RR eR ) cos( ) + n 2 C e = 1 2 (RL eL + RR eR ) sin( ) + e 2 C = 1 2 (RL eL RR eR ) +

(98)

jXL = j628f L = j(628 400 500) = j126 Next, calculate the reactance of the capacitor at 400 MHz Proceed as follows: jX C = j[1/(628f C )] = j[1/(628 400 0000200)] = j199 Finally, add the inductive and capacitive reactances to obtain the net reactance: jX = jXL + jX C = j126 + ( j199) = j 73 This is a pure capacitive reactance

(99)

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Problem 16-4 What is the net reactance of the aforementioned inductor and capacitor combination at the frequency f = 100 MHz

The signals n , e , and represent errors due to, for example, violation of the no-slip assumption These errors are not necessarily stationary and mutually uncorrelated random signals; however, unless some form of slip detection algorithm is incorporated, n , e , and would typically be modeled as independent random processes The length of the wheel radii RL and RR vary relative to their nominal values The variation depends on the type of tire as well as various unpredictable factors The wheel radii are modeled as RL RR = R0 + RL = R0 + RR (910) (911)

where R0 is the known nominal value of the wheel radii The error in the wheel radii will be modeled as scalar Gauss-Markov processes RL RR = R RL + L = R RR + R (912) (913)

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