Measurement and calculation method of multimeter

When using a multimeter to measure AC voltage or current, have you ever doubted the measurement results? When you are very confident in your circuit, you may doubt the accuracy of the multimeter's measurement. So where is the problem? Let's recall the mathematical formula for measuring AC signals with a multimeter.

1. The differences and similarities between average value and true effective value measurement:
First, understand the average value. Mathematically, the voltage average value is expressed using the following formula:

Where u(t) is the function expression of the signal, and T is the period of the signal. If we want to measure a standard sinusoidal signal, then this calculation method is both accurate and convenient. However, it is used to measure other AC signals (such as the square wave below):

Then use formula 4 to find the average value of the above formula. Assuming the period of the above signal is 2, then

Obviously the result is inaccurate. Therefore, it is concluded that when using the average value method to calculate communication signals such as square waves and sawtooth waves, there may be large errors.

So, is there a way to accurately measure AC signals such as non-sinusoidal waves? Therefore, the true effective value calculation method is introduced. The true effective value is the root mean square of current or voltage in one cycle, and its mathematical calculation formula is as follows:

Vrms indicates the true effective value of voltage, u(t) is the function expression of the signal, and T is the period of the signal. Using the above formula, first integrate the square of the signal and then take the square root. This method accurately calculates the effective value of various AC signals. Therefore, it is accurate to measure AC signals using the true effective value calculation method. When choosing a multimeter, be sure to choose a multimeter with true effective value measurement function.

2. AC+DC true effective value derived from the true effective value function:
Among various measured signals, there are often superimposed signals of AC and DC signals. In the past, the multimeters we used could only measure DC or AC signals separately, but could not measure the superimposed signals of DC and AC signals. So, how can we accurately measure the superimposed signals of AC and DC signals?

First of all, it should be understood that the superposition of the DC signal and the AC signal is not equivalent to the simple addition of the AC signal's true effective value and the DC signal. Take the DC signal u1(t)=1(v) and the AC signal u2(t)=sint as an example. The signal after the superposition of the two is expressed as: u(t)=1+2sint; the
true effective value result is u(t)=1.732, not 1+1.414=2..414. Substituting the superposition of the DC signal and the AC signal into the true effective value calculation formula yields

Among them, AC+DC indicates the true effective value of the superimposed signal, DC indicates the size of the DC signal, and ACrms indicates the true effective value of the AC signal, so that the superimposed signal of the DC signal and the AC signal can be accurately calculated. The AC+DC function is of great significance to the test of superimposed peak power. The distorted harmonic wave superimposed by DC can cause the transformer, generator, and engine to overheat, and also make the circuit breaker circuit easy to trip and fuse to blow. It cannot be ignored during measurement, so it is very necessary to use a multimeter with AC+DC true effective value measurement function (such as OI859CF handheld multimeter).

In a word, the multimeter measures the AC voltage, current and resistance through circuit transformation on the basis of the DC voltmeter. It is more accurate to use the true effective value calculation method to measure non-sinusoidal AC signals, which will help us to carry out research and experiments better.