For sinusoidal signals, the current flowing through a component and the voltage across it are not necessarily the same phase. How does this phase difference occur? This kind of knowledge is very important, because not only the feedback signals of amplifiers and self-excited oscillators need to consider the phase, but also the phase difference needs to be fully understood, utilized or avoided when constructing a circuit. This issue is discussed below.
First, we need to understand how some components are constructed. Second, we must understand the basic working principles of circuit components. Third, we must find out why the phase difference occurs. Fourth, we can use the phase difference characteristics of components to construct some basics. Circuit.
First, the birth process of resistance, inductance, and capacitance
After long-term observations and experiments, scientists have cleared up some truths, and often have unexpected accidental discoveries. For example, Roentgen discovered X-rays, and Madame Curie discovered radium radiation. These accidental discoveries have become great Scientific achievements. The same is true in electronics.
When scientists let electric current flow through a wire, they accidentally discovered the heat and electromagnetic induction of the wire, and invented resistance and inductance. Scientists also took inspiration from the phenomenon of triboelectricity and invented capacitors. The discovery of rectification and the creation of diodes are also accidental.
Second, the basic working principle of components
Resistance——electric energy → thermal energy
Inductance——electric energy → magnetic field energy, & magnetic field energy → electric energy
Capacitance-potential energy → electric field energy, & electric field energy → current
It can be seen that resistance, inductance, and capacitance are the components of energy conversion. The resistance and inductance realize the conversion between different kinds of energy, and the capacitor realizes the conversion of potential energy and electric field energy.
1.Resistance
The principle of resistance is: potential energy → current → thermal energy.
Potential energy (positive and negative charges) is stored at the positive and negative ends of the power supply. When the potential is applied to both ends of the resistor, the charge flows under the potential difference-a current is formed, and its flow speed is much faster than the disorderly free movement without potential difference There is more heat generated by a collision in a resistor or conductor.
The positive charge enters the resistor from the high-potential side, and the negative charge enters the resistor from the low-potential side, and the two perform neutralization inside the resistor. The neutralization effect makes the positive charge quantity present a gradient distribution from the high potential end to the low potential end inside the resistor, and the negative charge quantity presents a gradient distribution from the low potential end to the high potential end inside the resistor, thereby creating a potential difference across the resistance, which This is the voltage drop across the resistor. At the same current, the greater the resistance of the resistor to neutralization, the greater the voltage drop across it.
Therefore, R = V / I is used to measure the resistance of the linear resistance (the voltage drop is proportional to the current passed).
For AC signals, it is expressed as R = v (t) / i (t).
Note that there is also the concept of a non-linear resistor, and its non-linearity has a voltage effect type and a current effect type.
2.Inductance
The principle of inductance: inductance-potential energy → current → magnetic field energy, & magnetic field energy → potential energy (if there is a load, → current).
When the power supply potential is applied across the inductor coil, the charge flows under the potential difference-a current is formed, and the current converts the magnetic field. This is called the "magnetization" process. If the potential difference between the two ends of the magnetized inductor coil is cancelled, and the inductor is externally connected to a load, the magnetic field can be converted into electrical energy during the decay process (if the load is a capacitor, it is electric field energy; if the load is a resistor, it is current) This is called the "demagnetization" process.
The unit to measure how much the inductor coil is magnetized is the flux linkage—Ψ. The larger the current, the more the inductance coil is driven by the magnetic chain, that is, the magnetic chain is proportional to the current, that is, Ψ = L * I. For a given inductor, L is constant.
Therefore, L = Ψ / I is used to express the electromagnetic conversion capability of the inductor coil, and L is called the inductance. The differential expression of the inductance is: L = dΨ (t) / di (t).
According to the principle of electromagnetic induction, a change in magnetic flux produces an induced voltage. The greater the change in magnetic flux, the higher the induced voltage, that is, v (t) = d dΨ (t) / dt.
Combining the above two formulas: v (t) = L * di (t) / dt, that is, the induced voltage of the inductor is proportional to the change rate of the current (derivative to time). The faster the current changes, the higher the induced voltage.
3.Capacitance
The principle of capacitance: potential energy → current → electric field energy, electric field energy → current.
When the power supply potential is applied to the two metal plates of the capacitor, the positive and negative charges are concentrated to the two plates of the capacitor under the action of the potential difference to form an electric field, which is called a "charging" process. If the potential difference between the two ends of the charged capacitor is removed, and the capacitor is externally connected to a load, the charge at both ends of the capacitor flows away under its potential difference, which is called a "discharge" process. During the process of the charge accumulating to the capacitor and flowing away from the two plates of the capacitor, the flow of the charge forms a current.
Special attention should be paid to the fact that the current on the capacitor does not actually flow through the insulating medium between the two plates of the capacitor, but only the flow of charge from the outside to the two plates of the capacitor during the charging process, and the charge from the discharge process The flow formed by the two plates of the capacitor flowing away. In other words, the current of the capacitor is actually an external current, not an internal current, which is different from the resistance and the inductance.
The unit to measure how much the capacitor is charged is the charge number-Q. The larger the potential difference between the capacitor plates is, the more the charged plates are charged, that is, the number of charges is proportional to the potential difference (voltage), that is, Q = C * V. For a given capacitance, C is constant.
Therefore, C = Q / V is used to express the capacity of the capacitor plate to store charge, and C is called the capacitance.
The differential expression of the capacitance is: C = dQ (t) / dv (t).
Because the current is equal to the change in the number of charges per unit time, that is, i (t) = dQ (t) / dt,
The above two formulas are combined: i (t) = C * dv (t) / dt, that is, the capacitance current is proportional to the change rate (derivative of time) of the voltage on it.
Summary: v (t) = L * di (t) / dt
Shows that the change in current forms the induced voltage of the inductor
Pressure formation).
i (t) = C * dv (t) / dt indicates that the voltage change forms the external current of the capacitor (actually the amount of charge changes. If the voltage is constant, no external current of the capacitor is formed).
Third, the component changes the signal phase
First of all, we must remind that the concept of phase is for sinusoidal signals. There is no concept of phase for DC signals and non-periodic signals.
1.The voltage and current on the resistor are in phase
Because the voltage on the resistor v (t) = R * i (t), if i (t) = sin (ωt + θ), then v (t) = R * sin (ωt + θ). Therefore, the voltage and current on the resistor are in phase.
2.The current on the inductor is 90 ° behind the voltage
Because the induced voltage v (t) = L * di (t) / dt on the inductor, if i (t) = sin (ωt + θ), then v (t) = L * cos (ωt + θ).
Therefore, the current on the inductor is 90 ° behind the induced voltage phase, or the induced voltage is 90 ° out of phase with the current. Intuitive understanding: Imagine an inductor in series with magnetizing magnetization. From the magnetization process, the change of the magnetizing current causes the change of the magnetic flux, and the change of the magnetic flux generates the induced electromotive force and the induced current. According to Lenz's law, the direction of the induced current is opposite to that of the magnetizing current, which delays the change of the magnetizing current and makes the phase of the magnetizing current lag behind the induced voltage.
3.The current on the capacitor leads the phase by 90 °
Because the current i (t) = C * dv (t) / dt on the capacitor, if v (t) = sin (ωt + θ), then i (t) = L * cos (ωt + θ).
Therefore, the current on the capacitor is 90 ° ahead of the voltage, or the voltage is 90 ° behind the current.
Intuitive understanding: Imagine a capacitor connected in series with a resistor. Judging from the charging process, there is always the accumulation of flowing charge (ie, current) before the voltage change on the capacitor, that is, the current always leads the voltage, or the voltage always lags behind the current. The following integral equations reflect this intuition:
v (t) = (1 / C) * ∫i (t) * dt = (1 / C) * ∫dQ (t), that is, the accumulation of charge changes forms a voltage, so the phase of dQ (t) is ahead of v (t ); And the process of charge accumulation is the process of synchronous change of current, that is, i (t) and dQ (t) are in phase. Therefore i (t) is ahead of v (t).
Fourth, the application of component phase difference-understanding of RC Venturi bridge, LC resonance process
Regardless of the series resonance or parallel resonance of the RC Wen's Bridge or the LC, it is caused by the phase difference between the voltage and current of the capacitive or / and inductive capacitive elements, just like the beat of mechanical resonance.
When two sine waves with the same frequency and phase are superimposed, the amplitude of the superimposed wave reaches the maximum value. This is the resonance phenomenon, which is called resonance in the circuit.
When two sine waves with the same frequency and opposite phases are superimposed, the amplitude of the superimposed waves will be minimized, or even zero. This is the principle of reducing or absorbing vibration, such as noise reduction equipment.
When multiple frequency signals are mixed in a system, if two signals of the same frequency generate resonance, then the energy of other vibration frequencies in this system will be absorbed by these two signals of the same frequency and phase, thus acting as Filtering at other frequencies. This is the principle of resonance filtering in the circuit.
Resonance needs to satisfy both the same frequency and the same phase. The method of how the circuit selects the frequency by the amplitude-frequency characteristic was previously described in the RC Wen's Bridge. The idea of the LC series and parallel connection is the same as that of the RC. Let ’s take a look at a rough estimate of the phase compensation in the circuit resonance (more accurate phase offset is to be calculated) 1. The resonance of the RC Wien bridge (Figure 1)
If there is no C2, the current of the sinusoidal signal Uo changes from C1 → R1 → R2, and the Uf output voltage is formed by the voltage drop across R2. Because the branch current is phase-shifted 90 ° ahead of Uo by capacitor C1, this phase-leading current flows through R2 (resistance does not cause a phase shift!), So that the output voltage Uf voltage is 90 ° ahead of Uo.
C2 is connected in parallel with R2, and C2 takes the voltage from R2. Due to the hysteresis effect of the capacitor on the voltage, the voltage on R2 is also forced to lag. (But not necessarily 90 °, because there is also the effect of C1 → R1 → C2 current on the voltage on C2, which is Uf, but at the RC characteristic frequency, the Uf output phase is the same as Uo after C2 is connected in parallel.)
Summary: The parallel capacitance makes the voltage signal phase lag, which is called parallel compensation of voltage phase.
2. LC parallel resonance (Figure 2)
If there is no capacitor C, the sinusoidal signal u is induced by L to the secondary output Uf, and the voltage of Uf is ahead of 90 °; In the primary parallel capacitor C of L, the voltage on L is also forced to lag by 90 ° due to the hysteresis of the capacitor on the voltage. . Therefore, the Uf output phase is the same as u after C is connected in parallel.
3. LC series resonance (Figure 3)
For the input sinusoidal signal u, the capacitor C makes the current phase of the load R in the series circuit ahead of u 90 °, and the inductance L makes the current phase in the same series circuit lag another 90 °. Therefore, the output Uf is in phase with the input u.
Summary: (Note that the phase effect is not necessarily 90 °, it is related to other parts, and the specific calculation is required)
The series capacitor advances the phase of the series branch current, thereby affecting the output voltage phase. The parallel capacitor lags the voltage phase of the parallel branch, which affects the output voltage phase. The series inductance causes the phase of the series branch current to lag, thereby affecting the output voltage phase. The shunt inductance leads the shunt voltage of the shunt branch, thereby affecting the output voltage phase.
More concise memory:
Capacitors advance the phase of the current, and inductors advance the phase of the voltage. (Both refer to the current or voltage on the component)
Capacitance-current lead, inductance-voltage lead
