## Frequency Response

### Introduction

The frequency response shows the behavior of the test object during a frequency change. For almost all objects in electro-technology a frequency response can be measured. The frequency response contains two substantial characteristics, amplitude and phase. The amplitudes are noted vs. frequency and also the phase vs. to frequency. If amplitude response and phase response in a diagram are noted, this graph can be called also Bode plot. The term Bode plot originates from control engineering.

#### Amplitude Response

For the measurement amplitude response is a sinusoidal signal on the input of the amplifier, which becomes in its frequency continuously changed (sweeped). The amplitude of the input signal and the output signal amplifiers are noted. Both amplitudes of the respective associated frequency are set into the relationship output voltage to input voltage. The quotient from it is called gain. This procedure will become for each frequency repeated and the quotients registered in a coordinate system. The quotient is often formed for logarithm in the logarithmic relationship, 20 * to the basis 10 (Uout/Uin). A dimensionless unit develops decibel, shortened in dB. If the levels are referred not to resistances (e.g., 50, 75 or 600 ohms), often the designation applies dBV. for example corresponds 0 dBV = 1 V to RMS. (RMS root mean square originates from the English and designates the rms).

Examples:

x dBV = 20 * log (Urms out/Urms in)

-20 dBV = 20 * log ( 1 volt rms / 10 volts rms)

-4,43 dBV = 20 * log (3 volts rms / 5 volts rms)

0 dBV = 20 * log ( 1 volt rms / 1 voltv rms)

6,02 dBV = 20 * log ( 2 voltv rms / 1 volt rms)

20 dBV = 20 * log ( 10 volts peak / 1 volt peak)

40 dBV = 20 * log ( 333 volts peak to peak / 3.33 volts peak to peak )

The quotient in the brackets must remain always dimensionless, i.e. the units must away-shorten themselves. If these things for you are somewhat unusual, take a pocket calculator and check it, it brings exercise. As a noticing assistance a relationship of 10 subject always results in 20 dB. One of 100 results in 40 etc..

If you want to count again backwards, then that can be done simply in such a way:

-20 / 20 = 1 - afterwards 10 exp 1 = ratio 0,1  from output to input voltage (1/10=10)

-4,43 / 20 = -0.2215 - afterwards 10 exp -0,2215 = ratio 0,6  from output to input voltage (3/5=0,6)

0 / 20 = 0 - afterwards 10 exp 0 = ratio 1  from output to input voltage (1/1=1)

6,02 /20 = 0.301 - afterwards 10 exp 0.301 = ratio 2  from output to input voltage (2/1=2)

20 / 20 = 1 - afterwards 10 exp 1 = ratio 10  from output to input voltage (10/1=10)

40 / 20 = 2 - afterwards 10 exp 2 = ratio 100  from output to input voltage (333/3.33=10)

Those backwards computation returns the unitless relationship from output voltage to input voltage as result in each case.

#### Phase Response

For the measurement phase response is a sinusoidal signal on the input of the amplifier, which is continuously changed in its frequency (sweeped). Are noted the phase of the input signal and the output signal of the amplifier. The phase of the input signal serves as reference and is set for zero. The phase difference of the output signal for the input signal of the respective associated frequency is noted in a coordinate system

### Meaning of frequency response for a hifi amplifier

The frequency response is one of the most important sizes with an amplifier. It is one of the first sizes, which it applies to consider. From that amplitudes and the phase response is recognizable out:

• which is to be expected at linear distortions. Data in numbers in addition are not usual and in electro-technology also not defined. A procedure would have to be redefined and computed. This procedure most similarly, would be the measurement of the group delay time. That is the mathematical 1. Derivative of the phase response.

• Frequency ranges in those the amplifier some tones too quietly or too loud shows. The indication in addition takes place often in dB, e.g.. +-0.8 dB. This indication applies then usually to the entire audio range.

• Is the bandwidth how high? The indication up to which frequencies of the amplifiers still meaningfully transferred can.

• Overshooting behavior in the region of the range. Thus statements about the stability of the amplifier are possible. First conclusions on the behavior with difficult loads are possible.

• The exclusive frequency response states something, over the nonlinear distortions which can be expected. To the safety device of statements several frequency responses are necessarily noted, with different input amplitudes. Figure 1 shows the frequency response of the amplifier with a gain of 1000. To see are the amplitudes and the phase response. Figure 2 shows the amplitude response forest and meadows amplifiers. Noted with different input voltages. If the amplitude responses for different input signals are compared with one another, first tendentious statements about nonlinear distortions are possible. These here distorted, the amplitude responses do not lie diekt one above the other like them it should. This measurement in fig. 2 is related to differential a Gain/Phase measurement, important sizes for operation amplifiers, which are used for television's applications.

### Which frequency responses have hifi amplifier?

Different one, no generally valid statements possible. Some amplifiers reach 20 kHz -30 kHz range (particularly some large one), smaller one and middle amplifiers, some of it fly far beyond 100 kHz. A frequency response diagram not indicated by the manufacturer unfortunately always, often only the indication for the audio range e.g.. 10 cycles per second to 20 kHz +-0.2 dB. A short statement, however sufficiently in principle. For the indication of the range takes place then e.g.. -3 dB @ 100 kHz.

#### Further link to the topic:

What are Open Loop, Slew Rate and bandwidth

Measuring of amplitude response

Phaseshift (Measurement)