What is Zero Initial State? What is Zero Input? 10

Zero initial state: The initial energy storage of the dynamic element is zero. Zero input:

In the absence of an external excitation, the response is caused only by a non-zero initial state at the time of t=0. Depending on the initial state and circuit characteristics, this response decays exponentially over time.

The first-order circuit has only one dynamic element (capacitance or inductance), and if the dynamic element has stored energy (electrical or magnetic) at the moment of switching, then even if there is no excitation power supply in the circuit, after the switch, the dynamic element in the circuit will be discharged through the circuit, and a response (current or voltage) will be generated in the circuit, that is, zero input response.

For first-order circuits, the zero input response is the response caused only by the initial energy storage of the energy storage element.

Brief introduction. In addition to the response caused by the excitation, the "initial state" within the system can also cause the response of the system. In a "continuous" system, the initial state of the system is often provided by its internal "energy storage elements", such as a capacitor in a circuit that stores electric field energy, an inductor coil.

It can store magnetic field energy, etc. The state of energy stored by these energy storage elements at the beginning of the calculation of time constitutes the initial state of the system.

If the excitation of the system is zero, the response caused by the initial state alone is referred to as the "zero input response" of the system. A charged capacitor is discharged through a resistor, which is the simplest example of a system's zero-input response. The zero-input response of the system is completely determined by the characteristics of the system itself, and has nothing to do with the excitation of the system.

When a system is linear, its properties can be characterized by linear differential equations.

When represented, the zero input response is in the form of several exponential functions.

The sum of the same. The number of exponential functions is equal to the order of the differential equation, i.e. the number of "independent" energy storage elements contained in the system. Assuming that the system does not contain a power source inside it, then such a system is called a "passive system".

The zero-input response of the actual passive system gradually decays to zero over time.

The zero-input response is part of the homogeneous solution of the differential equations of the system.

The stability of a nonlinear system and the nature of the zero-input response depend not only on the structure and parameters of the system itself, but also on the initial state of the system.

Zero-state response: The energy storage components (capacitors, inductive components) of the circuit have no initial energy storage and are only reacted by external excitation. In some circuits with initial energy storage, for the convenience of solving, it is also possible to assume that the circuit has no initial energy storage, find its zero state response, and then add the full response of the vested circuit with the zero input response of the circuit.

When finding the zero state response, it is generally possible to list the relations of the circuit by using Kirchhoff's law according to the characteristics of the components of the circuit (capacitance voltage, inductance current, etc.), and then replace the differential equation of the circuit. The differential equation is used to write the characteristic equation of the system, and the form of the free response equation of the system can be solved by using its characteristic roots. The zero-state response is composed of a partial free response and a forced response, and the free response part has the same form as the obtained equation, plus the zero-state response form of the system obtained by the special connection. It can be solved using the impulse function coefficient matching method.

There is an initial copy state to have zero input bai

Response, cause and effect.

1.Zero input response, as the name suggests, is the response with the input of zhi0, why is there a response if the input of the dao is zero.

2.Because there is an initial state, why can the initial state exist, because the capacitor and inductor and other components in the system can be stored for energy.

3.The zero moment that we set, and it happens that they have energy at that moment, is the initial state.

A circuit that contains a separate energy storage element (capacitor or inductor) is called a first-order circuit.

If the input excitation signal is zero, only the response excited by the initial energy storage of the energy storage element is called the zero input response.

Conversely, the initial energy storage of the circuit is zero, and the response caused only by the excitation is a zero state response.

Dynamic circuits, power supplies. The initial energy storage of either the inductor or the capacitor can be used as an excitation to the circuit in response.

Zero input response, which is maintained only by the element's initial energy storage (the initial value is not 0, but at the same time there is no external excitation).

Zero-state response, when the initial energy storage of the element is in the zero state (the initial value is 0), the response after receiving an external excitation (the external excitation is not 0).

Zero input response: There is no external excitation, only the response generated by the initial state (the energy storage of the system at the beginning moment).

Zero state response: The role of the system's energy storage at the start time is not considered (the start state is equal to zero).

The zero state response is that the energy storage components (capacitors, inductive components) of the circuit have no initial energy storage, back.

The response is generated only by external stimuli. A zero-state response is a response caused by an external excitation source only in the absence of initial energy storage or a no-zero state.

A zero-input response is a response that is caused only by a non-zero initial state at the time of t = 0 in the absence of an external stimulus. It depends on the initial state and circuit characteristics, and this response decays exponentially over time.

That is, when the book says t=0, the input and output quantities and their derivatives are zero. Because of the differential nature of the Laplace transform, the weight transformation of the function differentiation is related to the initial value of the function and the initial value of each derivative, and if the initial condition is zero, then the transformation of the differential is relatively simple and has nothing to do with the initial value. As for the step function, there are several different ways to define it, in the Laplace transform, when t=0, the function value of the unit step function is not defined, which feels like it is deliberately set this way for the sake of zero initial condition.

For details, please see the following page.

Actually, you don't have to worry about this detail, the zero initial condition is mainly to make it easier to write the transfer function, and nothing else. lz can be thought of this way, in fact, the 0 point is artificially determined, you can shift the unit step function to the right by 1 unit, so that t=0 is the original t=-1, so that the zero initial condition is strictly observed. Despite this, the step is still a step, and the output is only one unit delayed from the original, nothing else changes.

If you think about it this way, don't you think that this detail is not important?

The zero-state response is the response of the circuit to an external excitation under zero initial conditions (zero initial energy storage for dynamic components).

Zero input response refers to the response generated by the initial energy storage of the dynamic component without an external excitation power supply in the circuit.

The zero input response is only the initial state response of the capacitive element, which is essentially the discharge process of the RC circuit;

The zero-state response is only the circuit response generated by the power excitation, which is essentially the charging process of the RC circuit.

Similarities: both find the change law of capacitance voltage UC when t>=0.

The zero state is 0 for both the starting voltage and the current. There is no voltage and current input with zero input.

From my current memory of circuits, it seems like this.

Zero-state response means that at t=0-, the voltage of the capacitor is 0 and the current of the inductor is 0

A zero-input response means that the input of the power supply is 0 at t=0-

In the first-order circuit, there is any energy storage device L or C, when the input is 0, only let the energy storage device release energy, and the input is corresponding to 0 in the state; On the contrary, when the input is not 0, the energy storage device voltage is 0, and the energy in the loop is provided by the input voltage, and the state is called 0 state correspondingly.

Zero: y(t) is nothing.

Zero loss: y(t) has to nothing.