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Experiment collection of University "Fundamentals of circuit analysis". Experiment 7 - Research on sinusoidal steady-state circuit

2022-07-02 15:45:00 【Computer programmer ape】

experiment 7、 ... and Research on sinusoidal steady state circuit

Catalog

1 The experiment purpose

2 Experimental instruments and equipment

3 Preview the experiment

4 Experimental requirements and precautions

5 Experimental principle

6 Experiment content and steps

7 Experimental report and thinking questions

1 The experiment purpose

1. understand R、L、C The relationship between the voltage and current at the component end .

2. Study the phasor relationship between voltage and current in sinusoidal steady-state circuit .

3. Learn how to use a dual trace oscilloscope to measure the phase difference of the same frequency signal .

2 Experimental instruments and equipment

A multimeter a

Integrated circuit test box a

Dual trace oscilloscope One

3 Preview the experiment

1. Review the knowledge of sinusoidal steady-state circuit .

2. Understand the content and principle of this experiment , Calculation table 1-2、 surface 1-3 Theoretical value of .

4 Experimental requirements and precautions

1. In order to improve the measurement accuracy , Reduce the interaction between instruments , When connecting circuits and measuring, pay attention to sending function signals as far as possible

Generator 、 AC millivoltmeter 、 The oscilloscope and the grounding terminal of the experimental circuit are connected together .

2. When measuring the phase difference between two waveforms , The circuit should be correctly connected , Pay special attention to the correct selection of the common contact of two pairs of input lines of the oscilloscope

How to connect .

5 Experimental principle

5.1 In a dynamic circuit with sinusoidal excitation , Its voltage 、 The current is a sinusoidal signal with the same frequency as the excitation signal , It is called sinusoidal steady state electricity

road .

5.2 The analysis method of sinusoidal steady-state circuit adopts phasor analysis , Voltage in the circuit 、 The current vector still satisfies the Kirchhoff voltage 、

Current law , namely

5.3 When the current on the component is consistent with the voltage reference direction ,R、L、C The volt ampere relationship of the element is

（1） resistance R The relationship between the sinusoidal voltage at both ends and the sinusoidal current flowing through the resistance conforms to the formula $\large \dot{U}=\dot{R}\dot{I}$ , The waveform of voltage and current

Consistent phase , Pictured 1-1 Shown .

chart 1-1 The voltage on the resistor is in phase with the current

（2） inductance L The relationship between the sinusoidal voltage at both ends and the sinusoidal current flowing through the inductor conforms to the formula $\large \dot{U}=Z_{L}\dot{I}$ , among , $\large Z_{L}=j\omega L$

, The phase of the voltage is ahead of the phase of the current 90°, Pictured 1-2 Shown .

chart 1-2 The phase lead current of the voltage on the inductor 90°

（3） capacitance C The relationship between the sinusoidal voltage at both ends and the sinusoidal current flowing through the capacitor conforms to the formula $\large \dot{U}=Z_{C}\dot{I}$ , among $\large Z_{C}=\frac{1}{j\omega C}$

, The phase of voltage lags behind the phase of current 90°, Pictured 1-3 Shown .

chart 1-3 The phase lag current of the voltage on the capacitor 90°

5.4 Sampling resistance

In the experiment , When observing the phase relationship between the terminal voltage of a certain branch and the current flowing , It is necessary to measure the waveform of voltage and current . from

When the oscilloscope observes the waveform, it is connected in parallel at both ends of the measured Branch , therefore , The waveform of voltage can be easily observed by oscilloscope , And electricity

The waveform of the flow cannot be observed directly with an oscilloscope . The usual method is to string a small resistance sample into the measured Branch

Resistance , Convert the waveform of the measured current into a voltage waveform that changes according to the same law , Then use the double trace oscilloscope to observe at the same time .

6 Experiment content and steps

6.1 measurement R、L、C The phase relationship between voltage and current on the component

（1） stay “ Dynamic circuit research module ” On the board , According to the figure 1-4 Connect the experimental circuit . Connect the output end of the signal source with 1P04、

1P05、1P06 Connected to a , send R、L、C The components are respectively connected to the circuit ; among ,1L2=15mH,1C2=0.015mF,

1R3=1KW; In order to facilitate the measurement of current waveform , Connect a 20W Sampling resistance of 1R2;1R2 One end 1P03 Pick up

To GND;

（2）DDS The signal source output provides sinusoidal AC signal , Its frequency is 8kHz, Effective value of amplitude U = 1V（ Use rivet hole line to DDS

The terminal is connected with the millivoltmeter terminal , adjustment DDS Signal source amplitude , Make the millivoltmeter read 1.00）. Oscilloscope CH1 Of “＋” Receive 1TP03

The test end ,“－” Receive 1P03 End , Measure the current passing through both ends of the inductor ; Oscilloscope CH2 Of “＋” Terminate 1P04,“－” End suspension

Don't pick up , Measure the voltage across the inductor ; Oscilloscope trigger source selection CH2 Trigger , take CH1 Transfer to 100mV/Div,CH2 Transfer to

2V/Div; At this time, the phase relationship between the voltage at both ends of the inductance and the current flowing through the inductance can be observed on the oscilloscope , Measurement requires

Read out the number of cells occupied by a period of sinusoidal signal A, And the number of cells occupied by the phase difference of the two waveforms B. Fill the measurement data in the table

1-1.

chart 1-4 measurement *R、L、C* Experimental circuit of phase relationship between voltage and current on components

（3） Map 1-4 Replace the inductance in with capacitance （ Signal source output DDS And 1P05 Connected to a , Oscilloscope CH2 Of “＋” Terminate

1P05）, Use a dual trace oscilloscope to observe the phase difference between the voltage at both ends of the capacitor and the current flowing through the capacitor . Fill the measurement data in the table

1-1.

（4） Map 1-4 Replace the capacitance in with resistance （ Signal source output DDS And 1P06 Connected to a , Oscilloscope CH2 Of “＋” Terminate

1P06）, Use a dual trace oscilloscope to observe the phase difference between the voltage at both ends of the resistance and the current flowing through the resistance . Finish the table 1-1.

explain ： In the picture R=20Ω It is to provide sampling resistance for measuring current . In the experiments , Use the voltage waveform on the sampling resistance to replace the current

The current waveform of the tested component , It is convenient to measure the phase difference .

surface 1-1 R、L、C The phase difference between voltage and current on the component

Phase difference between voltage and current		electric sense	electric Rong	electric Resistance
The reason is On value
Dual trace oscilloscope Measured value	B
	A
	Phase difference

Be careful ： When measuring , To reduce the measurement error , Adjustable number of cells occupied by sine wave period A To be close to 10 The integer of , Then read the number of cells occupied by the difference between the two waveforms B.

2. Research RL Phase relationship between voltage and current in series circuit

（1） stay “ Dynamic circuit research module ” On the board , According to the figure 1-5 Connect the experimental circuit . Output the signal source DDS Receive

1P04,1P06 Receive GND; among ,1L2=15mH,1R3=1KW;

（2）DDS The signal source provides sinusoidal AC signal , Adjust its output frequency to 8kHz, Adjust its output amplitude to make the voltage effective value U =

4V, Use an AC millivoltmeter to measure the voltage value on each component , Its vector diagram is shown in Figure 1-6 Shown , And calculate according to the measured value U、 Calculation

φ, Fill the measured data and calculated data in the table respectively 1-2.

（3） Measure the total voltage in the circuit with a dual trace oscilloscope U And total current I Phase difference of φ, Fill in the table 1-2.

surface 1-2 Study the phasor relationship between voltage and current

Measurement and calculation						The oscilloscope measures
	U	UR	UL	Calculation U	Calculation φ	A	B	measurement φ
Theoretical value	4 V
Measured value

3. Research RLC Phasor relation of series circuit

（1） stay “ Dynamic circuit research module ” Press the figure on the experimental board 1-7 Connect the circuit . Signal source output DDS Connect to 1P01,1P02

Receive GND;

（2） The adjustment method of the output amplitude of the signal source is the same as the previous experiment , The output frequency is adjusted to 8kHz and 15kHz, With AC milli

The voltmeter measures the voltage value of each component at two frequencies , Fill the measurement data in the table 1-3.

（2） The dual trace oscilloscope measures the total voltage in the series circuit U And total current I Phase difference of φ. Record the measured data in table 1-3 “ Oscilloscope measurement

The amount ” One column .

（3） According to the above circuit and the effective value data of each voltage measured by AC millivoltmeter , Calculate the total voltage U And total current I Phase difference of

φ, Fill in the table 1-3.

surface 1-3 Determination RLC A series circuit

f	AC millivoltmeter						The oscilloscope measures
f	U	UR	UL	UC	Calculation U	Calculation φ	A	B	measurement φ
8kHz Theoretical value	4V						——	——	——
8kHz Measured value
15kHz Theoretical value	4V						——	——	——
15kHz Measured value