The experimental circuit is as follows:

Components and parameters:

Resistors are RJ14 type resistors with an accuracy of 0.1%, R1=100kΩ, R2=R3=10kΩ, R4=12kΩ, R5=3kΩ.

There are two sets of capacitors for comparison: one is a CB4 type capacitor with a high Q value, with a capacity of C1=C2=14.66nF and Q>20000. The other group is the common CL type capacitor with a capacity of C1=C2=15.34nF and Q=220.

All the above resistance and capacitance parameters are tested by TH2816 digital bridge.

51Ω is a resistance that matches the signal source, and the 1uF capacitor is a straight-off capacitor to avoid measurement errors caused by misalignment of the operational amplifier. The measurement errors caused by these two devices are much smaller than the effects of component errors, so their effects can be ignored.

There are three operational amps for comparison:

LF353, the main parameter GBW=4MHz.

NE5532, the main parameter GBW=10MHz.

THS4052, the main parameter GBW=70MHz.

Test method and test instrument:

vi is generated by a signal generator, the output voltage vo is measured by a digital voltmeter, and then the central frequency of the band-pass filter and the frequency of two half-power points are obtained by changing the signal frequency, and the Q value of the filter is calculated.

The signal source is Tektronix AGF 1022, the output voltage is measured by Fluke 45 digital multimeter, and the input and output signals are monitored by oscilloscope.

Measurement results:

In the first group of experiments, CL type capacitors were used.

1.1, the operation amplifier adopts LF353, and the result is: f0=2077.0Hz, Q=17.66.

1.2, the operation amplifier adopts NE5532, and the result is: f0=2080.0Hz, Q=16.85.

1.3, the operation amplifier adopts THS4052, and the result is: f0=2079.8Hz, Q=16.57.

In the second group of experiments, CB4 capacitors were used.

2.1, the operation amplifier adopts LF353, and the result is: f0=2169.8Hz, Q=21.21.

2.2. The operation amplifier adopts NE5532, and the result is: f0=2173.7Hz, Q=20.09.

2.3. The operation amplifier adopts THS4052, and the result is: f0=2173.9Hz, Q=19.67.

Analysis and Conclusion:

According to the theoretical calculation, under the ideal conditions of the components, the center frequency of the first group of experiments is f0=2074.8Hz, and the center frequency of the second group of experiments is f0=2171.1Hz. The Q values of both experiments are the same and should be Q=20.

However, it is obvious that the above experimental results are different from the theoretical results. This difference is due to the non-ideal characteristics of the op amp and capacitor. The effect of resistance is relatively small, so the following is an analysis of the op amp and capacitance.

First, look at the impact of the op amp.

The results of both sets of experiments were arranged in order of frequency response from low to high. Obviously, the center frequency of the high frequency response of the op amp is also high (1.2 and 1.3 are somewhat reversed, which may be the cause of the measurement error), but the overall effect is not very large, at most one in two thousand. However, the operational amplifier frequency response has a greater impact on the filter Q value, and the operational amplifier frequency response changes from 4MHz to 70MHz, and the filter Q value can have a change of -6% to -7%.

Now look at the effect of capacitance.

Two different capacitors were used in the two experiments. The first group is the capacitors produced today, which usually have Q values between 100 and 300. The second group is a capacitor produced many years ago, due to the use of aluminum foil winding (now the production of evaporation of metal film), so its equivalent series resistance is very low, has a very high Q value (in the bridge measurement when the Q value has been jumping on the value of tens of thousands).

Compare two sets of experiments using the same op amp, such as 1.3 and 2.3.

Let’s start with the effect on the center frequency. The theoretical f0 of 1.3 is 2074.8Hz, and the measured f0 is 2079.8Hz, with an error of 0.24%. Theoretical f0=2171.1Hz, measured f0=2173.9Hz, the error is 0.13%. It can be seen that the Q value of the capacitor does affect the frequency of the filter, but the effect is not very large.

Looking at the effect on Q. The theoretical Q value of both sets of filters is 20. The measured value of 1.3 is Q=16.57, and the error with the theoretical value is -17%. The measured value of 2.3 is Q=19.67, and the error from the theoretical value is -1.7%. The difference between the two is 10 times greater!

In fact, the actual Q value of this filter can be estimated according to the relationship “reciprocal of the actual Q value = reciprocal of the theoretical Q value + reciprocal of the Q value of C1 + reciprocal of the Q value of C2”. According to this formula, the estimated value of the actual Q value of 1.3 is 16.92, and the estimated value of the actual Q value of 2.3 is 19.96, which are basically consistent with the measured value.

The following conclusions can be drawn:

In the actual production of this kind of active power filter, the bandwidth of the amplifier and the Q value of the capacitor will affect the center frequency and Q value of the filter. The center frequency is slightly less affected, but the Q value is greatly affected. The narrower bandwidth of the op amp will increase the Q value of the filter. A decrease in the Q value of the capacitor will cause the Q value of the filter to decrease.