Mechatronics Engineering MT-144 NETWORK ANALYSIS Mechatronics Engineering (03)

VOLTAGE AND CURRENT SOURCES IDEAL, REAL, INDEPENDENT AND DEPENDENT

ACTIVE & PASSIVE ELEMENTS

ACTIVE ELEMENTS : SOURCES The most important active (circuit) elements are voltage and current sources: • Independent sources – independent voltage source – independent current source • Dependent sources – dependent voltage source – dependent current source

INDEPENDENT VOLTAGE SOURCE It provides a specified voltage, independent of the current through the element

INDEPENDENT CURRENT SOURCE It provides a specified current, independent of the voltage across the element

DEPENDENT (Voltage & Current) SOURCES Dependent source It is a voltage or current generator whose source output quantity depends on another circuit variable (current or voltage)

DEPENDENT SOURCES (cont) There are four types of dependent sources: VCVS, VCCS, CCVS, CCCS Vx: controlling voltage, Ix: controlling current and a,b,c,d: are multiplying constants

DEPENDENT SOURCES (cont)

Dependent Sources (cont)… Dependent sources can deliver power in a circuit. The voltage or current of a dependent source depends on the current or voltage in other circuit elements. Diamond ==> Dependent (Diagrams are using different letters than the last slide)

RTh Calculation Example #2 Find the Thevenin equivalent with respect to the terminals a,b:

Comments on Dependent Sources A dependent source establishes a voltage or current whose value depends on the value of a voltage or current at a specified location in the circuit. Device model is used to model behavior of transistors & amplifiers To specify a dependent source, we must identify: The controlling voltage or current (mostly, to be calculated) The relationship between the controlling voltage or current and the supplied voltage or current The reference direction for the supplied voltage or current The relationship between the dependent source and its reference cannot be broken! Dependent sources cannot be turned off for various purposes e.g. to find the Thévenin RTh, or while doing analysis using Superposition etc.

IDEAL AND REAL SOURCES Ideal Sources In case of an ideal voltage source, the output voltage is constant at the specified value (Vs), no matter what current is drawn from the source. In case of an ideal Current Source, the output current is constant at the specified value (Is), no matter what is the voltage (applied due to the load-circuit / load), across this ideal current source.

Independent Sources Independent sources can deliver power in a circuit. An ideal source will have either a fixed voltage OR current independent of other elements in the circuit. What is the maximum power that can be delivered by an ideal Source ?

Real Sources In an ideal voltage source, the voltage is constant no matter what current is drawn from the source. In a real, practical voltage source (like a battery), however, the output voltage typically decreases as more and more current is drawn, as is shown in the figure. Typically a real source is “rated” for currents below a current i which corresponds to a voltage v ≥ 95% vs (region near vs in the figure). For this region, it is a good approximation to model the i-v characteristics of a real source with a straight line. The equation of this line is (using active sign convention): v = vs − Rsi

Real Sources (Cont) … The equation of this line is (using active sign convention): v = vs − Rsi The above approximate i-v characteristics of a real source is a Thevenin form and, therefore, a real source can be modeled with an ideal voltage source , vs, and a resistance Rs. Rs is called the internal resistance of the source (it is not a real resistor inside the real source) and is typically small (an ideal voltage source has Rs = 0) . The same arguments can be applied to “real” current sources. An approximate model for a real current source is in Norton form. Rs is again the internal resistance of the source (and again, it is not a real resistor inside the real source!). For a “real” current source, Rs is typically large ( an ideal current source has Rs→∞).

MORE ON DEPENDENT SOURCES Dependent or Controlled Sources Most analog electronic devices include amplifiers. These are four-terminal devices (two input and two output terminals). The voltage or current in the output terminals are proportional to voltage or current of the input terminals. We need a new circuit element in order to model amplifiers. These elements are “controlled” or “dependent” sources. There are four type of “controlled” sources

MORE ON DEPENDENT SOURCES Note that the element located in the input with the controlling current or voltage can be any element: a short circuit, an open circuit, or a resistor. When one encounters a circuit containing a controlled source, the first step is always to find the “controlling” voltage and current (v1 or i1 in the above figures). In some circuits, the control voltage or current is not located near the controlled source in order to simplify circuit drawing. This does not mean that the controlling element is separate from the controlled source. It is essential to always remember that controlled sources are four terminal elements. This means, for example, that you cannot have a sub-circuit which include the controlled source but not its controlling element.

MORE ON DEPENDENT SOURCES Controlled sources behave similar to ideal (or independent) sources. For example, in the voltage-controlled voltage source in the shown figure, the output voltage is μv1 no matter what current is drawn from the circuit. All analysis method developed so far (KVL and KCL, node-voltage and mesh current methods, superposition, etc.) can be used for circuits containing controlled sources, and by treating the controlled source similar to an ideal source. In node-voltage and mesh current methods, we need to write an “auxiliary equation” which relates the controlling parameter to node-voltage or mesh current methods as is seen in the examples below, on the next slide

MORE ON DEPENDENT SOURCES Example 1: Find vo using KVL and KCL: Substituting for ix from first equation in the second and noting vo = RLio, we get:

MORE ON DEPENDENT SOURCES Example 2:

Two more slides to refresh your RAM

Source Combinations ≡ ≡ Voltage sources in series can be replaced by an equivalent voltage source: Current sources in parallel can be replaced by an equivalent current source: v1 + – v1+v2 + – ≡ + – v2 ≡ i1+i2 i1 i2

Primary Circuit Analysis Methods MESH ANALYSIS (“Mesh-Current Method”) 1) Select M independent mesh currents such that at least one mesh current passes through each branch* M = #branches - #nodes + 1 2) Apply KVL to each mesh, expressing voltages in terms of mesh currents => M equations for M unknown mesh currents 3) Solve for mesh currents => determine node voltages NODAL ANALYSIS (“Node-Voltage Method”) 0) Choose a reference node 1) Define unknown node voltages 2) Apply KCL to each unknown node, expressing current in terms of the node voltages => N equations for N unknown node voltages 3) Solve for node voltages => determine branch currents *Simple method for planar circuits A mesh current is not necessarily identified with a branch current.