HW4_Soln

# HW4_Soln - Masnari/Escuti/Brickley ECE 200 Fall 2008...

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Masnari/Escuti/Brickley ECE 200 – Fall 2008 – Homework 4 Basic DC Circuits with Diodes and Capacitors 1. [12 pts] Find the minimum voltage V x needed to keep the diode ‘on’. Assume the diode has a turn-on voltage of 1 V. In order to determine the minimum voltage min X V required to keep the diode ‘on’, we must determine the condition that must exist as we change X V so that the diode goes from ‘off’ to ‘on’. To do that, we assume that the diode is ‘off’ which implies that the voltage at node A with respect to ground is V V A 1 < and 0 = D I . As X V increases it will eventually cause A V to just barely reach V 1 at which point the diode is turned ‘on’, but the current D I through the diode will still be 0. So at that instant we have: (1) 0 ) 2 ( 3 : 1 = Ω A loop left V I K V KVL where V V V A 1 = = γ Thus mA K V V I 2 2 1 3 1 = Ω = . (2) 0 : 2 1 = D A node I I I KCL where 0 = D I so that mA I I 2 1 2 = = . (3) 0 ) 8 ( : min 2 = Ω X A loop right V I K V KVL where mA I and V V A 2 1 2 = = . Thus we have V mA K V X 17 ) 2 ( ) 8 ( 1 min = Ω = . In summary, diode is ‘off’ when 0 17 = < D X I V V and diode is ‘on’ when 0 17 D X I V V .

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2. [10 pts] Consider the circuit shown below. The diode has a turn-on voltage of 1 V. a) Determine the state of the diode (i.e. is it ‘on’ or ‘off’?). Note: You must clearly show all your work including any neatly drawn equivalent circuits that you might use. R 1 R 2 3 k Ω 1 k Ω I x 4 V 1.5 V Assume that the diode is ‘on’ in which case our KVLs and KCL can be written as: (1) 0 ) 3 ( ) 1 ( 4 : 2 = Ω Ω I K I K V KVL X loop left (2) 0 5 . 1 ) 3 ( : 2 = Ω V V I K KVL loop right γ where V V 1 = (3) 0 : 2 = D X A node I I I KCL We can solve Eq. (2) to get mA K V V I 833 . 0 3 5 . 1 1 2 = Ω + = so that Eq. (1) becomes mA K mA K V I X 5 . 1 ) 1 ( ) 833 . 0 ( ) 3 ( 4 = Ω Ω = . We can now solve Eq (3) to give mA mA mA I I I D X D 667 . 0 833 . 0 5 . 1 = = = . Thus since 0 > D I , the current flowing through the diode is in the proper direction indicating that our assumption of the diode being ‘on’ is correct. b) Use the state of the diode found in part (a) to find the current I x flowing through R 1 . As determined in part (a), the current flowing through 1 R is mA I X 5 . 1 =
3. [14 pts] Assuming that the turn-on voltage for the diodes in the circuits shown below is 0.7 V: a. Determine if the diode is ‘on’ in each circuit. b. Find the currents I 1 , I 2 and I D in each circuit.

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