28 Questions
What is the mode of conduction if πΌπ > 57.5Β°?
Discontinuous Mode
What is the value of ππ (ππ‘) if ππ‘ = 220Β°?
16.73 A
What is the value of πΌπ?
231Β°
What is the value of ππ,ππ?
63 V
What is the value of πΌπ,ππ?
6.3 A
What is the value of π πΉππ?
0.51
What is the value of ππ?
196.3 V
What is the value of ππ,ππ?
185.6 V
What is the value of π πΉπ£π?
2.94 V
What is the value of πΌπ?
7.072 A
What is the condition for the output current to be continuous in a single-phase full-bridge controlled rectifier?
io wt > 0 for all t
During which period do T1 and T2 conduct in a single-phase full-bridge controlled rectifier?
Ξ±f < Οt < Ξ±f + Ο
What is the expression for the load current io in a single-phase full-bridge controlled rectifier?
io = io,N + io,F
What is the expression for the natural response io,N in a single-phase full-bridge controlled rectifier?
io,N = Ae^(-L/R)t
What is the expression for the forced response io,F in a single-phase full-bridge controlled rectifier?
io,F = (Vp / Z) sin(Οt - β )
What is the expression for the impedance Z in a single-phase full-bridge controlled rectifier?
Z = β(R^2 + ΟL^2)
What is the expression for the phase angle β in a single-phase full-bridge controlled rectifier?
β = tan^(-1)(ΟL / R)
What is the boundary condition used to find the constant A in a single-phase full-bridge controlled rectifier?
io(Οt = Ξ±f) = io(Οt = Ξ±f + Ο)
What is the final expression for the load current io,C in a single-phase full-bridge controlled rectifier?
io,C = (Vp / Z) sin(Οt - β ) + Ae^(-t/L*R)
What are the values of the resistor and inductor in the RL load of the example problem?
R = 10Ξ©, L = 50mH
What is the minimum firing angle required for a rectifier to operate in continuous conduction mode?
57.5Β°
In a discontinuous-current mode, what happens to the output current before Οt = Ξ±f + Ο?
It reduces to zero
What is the expression for the output current io(Οt) in a discontinuous-current mode?
VP sin(Οt - Ξ±f - β ) / Z
What is the condition for a rectifier to operate in continuous conduction mode?
Ξ±f < 57.5Β°
What is the expression for the average output voltage Vo,dc in a discontinuous-current mode?
(Vp / Ο) sin(Ξ±f - Ξ±e)
In Example 3, what is the value of the inductor in the RL load?
50mH
What is the frequency of the AC source in Example 3?
50Hz
What is the firing angle set to in Example 3?
90Β°
Study Notes
Single-Phase Full-Bridge Controlled Rectifier with RL Load
- Also known as 2-pulse converter or phase-controlled bridge rectifier
- Converter current is continuous if output current is always positive: i_o(Οt) > 0 for all t
Continuous-Current Mode
- T1 and T2 conduct for Ξ±f < Οt < Ξ±f + Ο, while T3 and T4 conduct for Ξ±f + Ο < Οt < Ξ±f + 2Ο
- Load current satisfies the equation: v_o = v_s = Vp sin(Οt)
- Current is found by solving the DE: d_io/dt = (Vp sin(Οt) - R_io)/L
- The complete solution of this equation has the form: i_o = i_o,N + i_o,F
- i_o,N = Ae^(-t/Ο) and i_o,F = (Vp/Z) sin(Οt - β )
- Z = β(R^2 + Ο^2L^2) and β = tan^(-1)(ΟL/R)
RL-Load Current (i_o,C)
- The complete expression is: i_o = Ae^(-t/Ο) + (Vp/Z) sin(Οt - β )
- To determine A, consider the boundary condition: i_o(Οt = Ξ±f) = i_o(Οt = Ξ±f + Ο)
- Gives A = (2Vp sin(Ξ±f - β ))/Z e^(tanβ - 1)
Discontinuous-Current Mode
- In this case, the output current reduces to zero before Οt = Ξ±f + Ο and the converter goes to state zero (ALL 4 SCRs OFF) until the next triggering
- Output current is determined by applying the initial condition (i_o(Οt = Ξ±f) = 0)
- i_o(Οt) = (Vp/Z) [sin(Οt - β ) - sin(Ξ±f - β ) e^((Οt - Ξ±f)/tanβ )] for Ξ±f < Οt < Ξ±e
- V_o,dc = (Ο/2) (Vp e^(-Ξ±f/tanβ ))/Z for discontinuous conduction mode
Examples
- Example 1: Single-phase full-bridge rectifier supplied from a 220V, 50Hz AC source and operates in continuous mode supplying an RL load with 50mH inductor and 10β¦ resistor. The firing angle is set to 45Β°.
- Example 2: Show that the rectifier in Example 1 is operating in continuous conduction mode.
- Example 3: Single-phase full-bridge rectifier supplied from a 220V, 50Hz AC source and operates in discontinuous mode supplying an RL load with 50mH inductor and 10β¦ resistor. The firing angle is set to 90Β°.
This quiz covers the working principles and characteristics of a single-phase full-bridge controlled rectifier with an RL load, including its continuous current mode operation and load current equation.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
