In the process of learning and researching electronic circuits, we often see abbreviations such as DC and AC.
DC is the abbreviation for Direct Current, which refers to the current with a unique direction of charge flow. The direction of direct current is constant.
AC is the abbreviation for Alternating Current, which refers to the current that undergoes periodic changes in both intensity and direction, with an average value of zero within one cycle.
In AC circuits, there is a phase difference between current and voltage, which is the leading and lagging of the current.
The phase difference between current and voltage refers to the temporal difference in their waveforms at the same frequency, usually expressed in terms of angle or time. The magnitude and direction of phase difference depend on the type and parameters of components in the circuit.
In AC circuits, we can observe the following phenomena:
When the load that consumes current is mainly a resistive load, there is no phase difference between the current curve and the voltage curve, and the current is in phase with the voltage.
When the load that consumes current is mainly capacitive, the current leads the voltage, and the phase difference between the current and voltage is positive.
When the load that consumes current is mainly an inductive load, the current lags behind the voltage, and the phase difference between the current and voltage is negative.
The leading and lagging here generally refer to Peak or Zero Crossing. Taking the peak value as an example, current leading voltage refers to the occurrence of the peak value of current leading voltage.
The relationship between current and voltage of capacitors
A capacitor is two metal plates separated by an insulator. For DC signals, capacitance is equivalent to an open circuit. Only when the voltage at both ends of the capacitor changes, will there be current flowing in or out of the capacitor. Because if there is a certain pressure difference between the two ends of the capacitor, it is because there are some extra electrons on one side of the metal plate, while holes are formed on the other side of the metal plate due to the lack of electrons, which generates voltage
If you want to change the voltage at both ends of the capacitor, you must change the amount of charge on the metal plates on both sides. So when we change the voltage at both ends of the capacitor, we are actually moving the charges at both ends, which forms the flow of current.
Capacitors allow AC signals to pass through, but for DC signals, they are equivalent to a short circuit. Let's take a closer look at how this happened.
If the voltage at both ends of the capacitor remains constant and does not change over time, it means that the total amount of charge at both ends of the capacitor has not changed, and without any change in charge, no current will be generated.
If we apply an AC signal to both ends of the capacitor, when the voltage reaches its peak, the tangent of the waveform is almost horizontal, and the change in charge is very small, so we can say that the current is basically zero at this time.
The relationship between current and voltage of inductance
An inductor is a coil (usually wrapped around a ferromagnetic object).
For DC, the ideal inductance has zero resistance. Anything with ideal zero impedance, regardless of the current, if the current remains constant, its voltage difference at both ends is zero.
But how does the voltage difference between the two ends of an inductor occur?
If you change the current flowing through the inductor, the inductor will generate a new current, or a voltage will be generated at both ends of the inductor, which attempts to resist the change in current.
That is to say, for an inductor, it tends to maintain a constant current passing through it.
If the current flowing through the inductor remains constant or small, then the voltage difference between the two ends of the inductor is zero or very small. When the current changes greatly, the voltage at both ends of the inductor will also increase.
The induced electromotive force of an inductor is directly proportional to the rate of change in current. The faster the current changes, the greater the induced electromotive force, and the greater the pressure difference between the two ends of the inductor
experiment
The learning of analog circuits requires a combination of theory and practice, which complement and promote each other, and neither is indispensable.
We can use an oscilloscope to observe the waveform and phase difference of current and voltage in the circuit. An oscilloscope is an instrument that can display images of voltage changes over time, and can be used to measure parameters such as voltage, current, frequency, phase, etc.
Due to the author's poverty, they cannot afford to buy a current sensing probe. In order to measure current using an oscilloscope voltage probe, we need to use a Current Sensing Resistor, which is a resistor with a small resistance value that can convert current into voltage for the oscilloscope to measure. The resistance value of the current induction resistor should be as small as possible to minimize its impact on the circuit, generally not exceeding 1/10 of the impedance of the tested equipment.
The experimental circuit is as follows:
I used a 100 ohm resistor. Measure the voltage difference on both sides of the resistor using an oscilloscope CH2, as the relationship between the voltage and current at both ends of the resistor is always in phase. Namely, as the voltage rises, the current rises; Voltage decreases, current decreases. So this 100 Ω resistor is essentially a current sensing resistor, because the voltage at both ends of the resistor is proportional to the current passing through it.
The oscilloscope CH2 measures the voltage of the tested component to ground, and we will measure the phase difference of the resistance, capacitance, and inductance components separately.
The constructed experimental circuit is as follows:
The following figure shows the waveform when the DUT is a resistor:
The frequency of the signal generator is 1MHz, the peak to peak value of the output signal is 2V, and the input impedance of both channels of the oscilloscope is 1M Ω.
CH1 is yellow, CH2 is blue. CH1 measures voltage, while CH2 measures current.
The actual attenuation of the CH1 probe is 1/10, and the probe attenuation ratio set by the CH1 oscilloscope is 10X, so the oscilloscope CH1 displays the actual voltage.
The actual attenuation of the CH2 probe is 1/1, which means there is no attenuation, and the actual voltage level is 100mV. I set the attenuation ratio of the oscilloscope to 0.01X in units of A, which makes it look more convenient. The 1mA gear is not very accurate, we mainly look at the phase difference.
From the above waveform, it can be seen that there is no phase difference between the voltage waveform and the current waveform.
Measuring capacitance
We replace the tested device with a capacitor:
Note that the capacitive impedance of a capacitor to a 1MHz frequency signal is at least 1000 Ω to reduce the impact of current induced resistance on the circuit.
According to the capacitance calculation formula:
I have selected a 160pF capacitor here, and its capacitance at a signal frequency of 1MHz is:
Xc=1/(2 x 3.141592653 x 1 MHz x 160 pF)=995 Ω
How to calculate capacitive impedance Please search according to the webpage:
The measured waveform is as follows:
The yellow waveform represents voltage, and the blue waveform represents current. It can be seen that there is a phase difference between the current waveform and the voltage waveform, with the current peak leading the voltage peak. The phase difference is approximately 200ns.
In capacitive circuits, the phase difference is inversely proportional to the size of the capacitance, and the larger the capacitance, the smaller the phase difference.
Measure inductance
We replace the device under test with an inductor.
The inductance I have chosen is 151 uH, and according to the inductance calculation formula:
The impedance of 150uH to a 1MHz frequency signal is:
XL=2 *. 3141592653 * 1 MHz * 150uH=949 Ω
The measured waveform is:
The yellow waveform represents voltage, and the blue waveform represents current. It can be seen that there is a phase difference between the current waveform and the voltage waveform, and the current peak lags behind the voltage peak. The phase difference is approximately 200ns.
In inductive circuits, the phase difference is directly proportional to the size of the inductance, and the larger the inductance, the greater the phase difference.
summarize
Capacitors and inductors for AC signals
In capacitors, the current leads the voltage
In an inductor, the current lags behind the voltage
The relationship between current and voltage of capacitors
A capacitor in a DC circuit is equivalent to an open circuit, and only when the voltage changes will there be current flowing through it
The current is very small when the voltage remains constant or changes slowly, while the current is maximum when the voltage changes the fastest
The relationship between current and voltage can be represented by two sine waves with phase differences, where the current waveform leads the voltage waveform
The relationship between current and voltage of inductors
An inductor in a DC circuit is equivalent to zero resistance, and regardless of the current, the voltage at both ends is zero
By changing the current in the inductor, a voltage can be generated on the inductor, which attempts to resist the change in current
The relationship between voltage and current can be represented by two sine waves with phase differences, where the current waveform lags behind the voltage waveform
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