Lecture 06

Two models of actual power source and equivalent transformation

Two models of actual power supply and equivalent transformation�

• Actual voltage source model

VCL

Note:

• A good voltage source requires that R_s be as small as possible.
• Because the internal resistance is very small, an actual voltage source cannot be short-circuited;

Otherwise, the current can be very large and can burn the power supply.

Two models of actual power supply and equivalent transformation�

• Actual current source model

VCL

Note:

• A good current source requires that R_s be as large as possible.
• Because the internal resistance can be very large, an actual current source cannot be open-circuited;

Otherwise, the voltage can be very large and can burn the power supply.

Two models of actual power supply and equivalent transformation�

• Equivalent transformation of actual voltage source and current source: The relationship between port voltage and current remains unchanged before and after transformation.

i = u_s/R_su – u/R_su

i_s = u_s/R_su (u_s = i_s*R_si)

R_si = R_su

• Equivalence is for external circuits, not for internal circuits.

• Ideal voltage source and ideal current source cannot be converted to each other.

Two models of actual power supply and equivalent transformation

• Equivalent transformation of dependent voltage source and dependent current source:

voltage controlled

current source (VCCS)

current controlled

current source (CCCS)

Two models of actual power supply and equivalent transformation

• Equivalent transformation of dependent voltage source and dependent current source:

voltage controlled

voltage source (VCVS)

R_Su

KCL: i = gu_c – u/R_si

Two models of actual power supply and equivalent transformation

• Example

5A

4Ω

3Ω

7Ω

2A

i=?

5A

4Ω

3Ω

7Ω

2A

i=?

• Example

• Example

Convert the circuit into a serial connection of a voltage source and a resistor

• Example

Convert the circuit into a serial connection of a voltage source and a resistor

• Example

KVL: 60 + i*6 + i* 4 – 30 + i*10 = 0 🡪 i=-1.5A

• Example

KVL:

i₁ = (u_s – (γi₁/R₃ * R₂//R₃))/(R₁ + R₂//R₃)

Input resistance

Circuit without independent power supply (may include dependent source)

​

+

-

i

u

Input resistance:

R_i=u/i

Methods:

• When only containing resistors, one can apply VCL and Y-△ transformation to obtain Ri
• Otherwise, one can apply an additional current source or voltage source to calculate Ri.

Input resistance

• Example

Note:

• Set the independent source in the circuit with independent power supply to zero.
• The voltage source is replaced by a short-circuit branch, and the current source is replaced by an open-circuit branch.

Input resistance

• Example

u

KVL:

u=6i₁ + 3i₁=9i₁

R_i = u/i = u/(i₁+i₂) = u/(i₁+0.5i₁) = 6Ω