NF Frequency Response Analyzer FRA tecknical guide #NihonDenkei #denkei

1. Frequency Response Analyzer Technical Guide
Measurement Principle and How to Measure Various Frequency Response
TECHNICAL
GUIDE
Frequency Response Analyzer

2. 1 What Is Frequency Response?
Transfer characteristic Spectrum and network
How physical quantity such as electricity, heat, and
vibration transfer on the device under test is called
“transfer characteristic” . This is an important pa-
rameter to understand the behavior of the device
under test.
Instruments that measure frequency response are
roughly classified into two types according to their
function and purpose.
These two types of measuring instruments may
look quite similar. However, as stated above, the
target to be measured is completely different. In
network measurement, an analyzer that has an os-
cillator inside is used. Frequency response analyzer
(FRA) conducts, needless to say, the network mea-
surement.
(1) Spectrum measurement ... Measures “signals”
Frequency Response is measured with spec-
trum analyzers or FFT analyzers. These instru-
ments measure level (spectrum) of frequency in
the measured signal.
(2) Network measurement ... Measures “system”
Frequency Response is measured with network
analyzers or frequency response analyzers
(FRAs). These instruments measure frequency
dependency in the relation between input and
output of the device under test.
Analyzer
Analyzer
Measured Signal
?
?
Measured SUT
Frequency Response
For direct current, transfer characteristic may be
defined simply by ratio (gain). However, with actual
device under test, the transfer characteristic
changes with frequency. In addition, for alternating
current, phase difference between input and output
may be involved as well as ratio.
The change of transfer characteristic with
frequency (gain, phase) is called frequency
response function. In general, this is called “fre-
quency response” in short.
With audio amplifiers, a parameter such as amplifi-
cation factor corresponds to transfer characteristic.
With temperature sensors, the relation between
heat (input) and electrical signal (output) is the
transfer characteristic. Electrical impedance is
given by the ratio of voltage and current and thus, if
we consider current as input and voltage as output,
impedance characteristic is also a transfer charac-
teristic in wide sense.
Output
DUT
Input
Electricity
Heat
Vibration
etc ...
Electricity
Heat
Vibration
etc ...
Transfer Characteristic = Output/lnput
Frequency Response Analyzer FRA51615
Content
1. What Is Frequency Response? · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 1
•Transfer characteristic •Frequency Response •Spectrum and network
2. Instruments That Measure Frequency Response
1. Oscillator + AC Voltmeter · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 2
2. Network analyzer · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 2
3. FFT Analyzer + Signal Source · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 3
4. FRA (Frequency Response Analyzer) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 3
5. Differences in measurement methods · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 4
6. What cannot be done with FRA? · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 4
7. Frequency range of measuring instruments · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 4
3. Mechanism of FRAs (Frequency Response Analyzers)
1. FRA block diagram · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 5
2. Overview and functions of each section · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 5
2.1 Signal source · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 5
2.2 Input coupling · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 6
2.3 Auto ranging · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 7
2.4 DFT operation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 8
2.5 Integrals and S/N · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 9
2.6 Delayed Measurement · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 9
2.7 Amplitude compression · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
2.8 Frequency axis slow speed high density sweep · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
2.9 I/O isolation · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 11
4. Measurement Example Using FRA
1. Gain-phase measurement example · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 12
•Frequency Response measurement of filter
•CMRR measurement of differential amplifier
•Tip s to reduce errors
2. Impedance measurement example · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 14
•Impedance measurement of electrolytic capacitor
•Output impedance measurement of switching power supply
•Impedance measurement of quartz oscillator
•Tips to reduce errors
3. Servo measurement example · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 19
•Loop gain measurement of switching power supply
•Open loop gain measurement of operational amplifier
•Tips to reduce errors
5. FAQ-Frequently Asked Questions · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 24
1

3. 2 Instruments That Measure Frequency Response
1. Oscillator + AC Voltmeter
There are systems using various methods as instru-
ments to measure frequency response (network
characteristic). Typical systems and characteristics
are described here.
In this method, input and output voltage of the SUT
(System Under Test) is measured with AC voltmeter
and divided to calculate gain. While this is the most
inexpensive and easiest method, there are the fol-
lowing disadvantages.
•Susceptible to noise and distortion
Noise and distortion components are also mea-
sured as they are.
This will result in a great measurement error
if internal noise of SUT or gain is great.
•Phase is unknown
It is not impossible to measure phase by observ-
ing the waveform of input/output with oscillo-
scope and by using or zero cross timing.
However, the precision will not be sufficient as
“measurement”.
•Troublesome and time-consuming measurement
The measurement requires the repetition of
changing oscillator frequency, measuring input
and output voltage, and doing division to calcu-
late gain. Therefore, the more frequency points
are to be measured, in proportion, the more trou-
blesome the measurement will be.
This is a general measuring instrument for high fre-
quency (tens of kHz and more). The output of the
bandpass filter where center frequency follows the
oscillating frequency of the internal sine-wave os-
cillator is detected and measured. Gain and phase
are measured by sweeping the oscillating frequen-
cy. Although there are many products available, it
is not recommended for measurement at low fre-
quency because the measurement will be extreme-
ly slow at low frequency.
Also, this instrument targets high frequency,
and the maximum signal level that can be mea-
sured is limited to a few volts.
2. Network Analyzer
SUT
Oscillator AC Voltmeter
DUT
Vector
Operation
Display
Detection
BPF
3. FFT Analyzer + Signal Source
FFT analyzers that have a signal source and 2 or
more channels of inputs to be analyzed can mea-
sure frequency response. It is the characteristic of
FFT analyzers that they can measure transfer char-
acteristic in wide range of frequency all at the same
time by using a signal source that contains wide
frequency components such as random noise and
impulse. They cover the measurement range of DC
to approximately 100 kHz. However, the following
disadvantages are present.
•Maximum dynamic range of approximately 96 dB
Most of the time, dynamic range of around 96 dB
is not sufficient for measurements such as servo
measurement. This means that correct measure-
ment is disturbed by noise.
•Limited frequency resolution
Due to characteristics of FFT, measurement fre-
quency resolution is determined by (AD sampling
frequency/Number of sampling points). For exam-
ple, if sampling frequency is 204.8 kHz with 2,048
sampling points, frequency response with 100 Hz
resolution can be obtained in the range between
DC and 102.4 kHz. If more detailed data with res-
olution finer than 100 Hz is desirable, the only
method is to increase the number of sampling
points. However, 2,048 sampling points is the
ceiling figure for commercially available FFT ana-
lyzers.
•Not suitable for measurement in wide frequen-
cy range
In wide frequency range, equally-spaced linear
measurement data with frequency as an axis will
be obtained. When displaying this graph on loga-
rithmic scale, the graph will be unnatural, too non-
dense at low frequency and too dense at high fre-
quency.
While FFT analyzers measure wide range of fre-
quency in a single measurement, FRAs can only
obtain data of gain and phase of a single frequency
in a single measurement. Although it may seem to
be inefficient for measurement, this analyzer can
solve the problems FFTs have.
•Great dynamic range
Because FRAs measure only a single frequency in
a single measurement, measurement range can
be changed to optimum according to the frequen-
cy to be measured. With measurement range vari-
able width in addition to dynamic range of A/D
converter (around 96 dB), quite a great dynamic
range can be secured.
DUT
FFT
Operation
Display
A/D
A/D
Signal
Source
4. FRA (Frequency Response Analyzer)
DUT
DFT
Operation
Display
A/D
A/D
2 3

4. •No limit for frequency resolution
Unlike FFTs, there is no measurement frequency
resolution determined by sampling rate and
memory length. The resolution is determined only
by the resolution of the internal oscillator. In the
case of FRA5096, measurement can be conduct-
ed with resolution of 0.1 mHz in the entire mea-
surement range between 0.1 mHz and 15 MHz.
•No frequency range
With FFTs, frequency range and frequency resolu-
tion are closely related. However, there is no fre-
quency range in FRAs. Sweep type allows you to
conduct logarithmic sweep as well as linear
sweep and thus, equally-spaced logarithmic data
can be obtained even in the measurement that
covers more than 9 decades (1 mHz to 1 MHz).
The differences among 4 methods to measure fre-
quency response previously described are shown
in the figure below.
FFTs measure the data over wide frequency
range in a single measurement. The other methods
measure only a single frequency component in a
single measurement and draw a graph of frequency
response by changing frequency to be measured.
5. Differences in measurement methods
As described, FRA is the best choice for measuring
frequency response in mHz to MHz order.
However, because this system is specialized
in measuring frequency response, there are some
functions FRAs cannot provide.
•Cannot measure direct current
FRAs have no function to measure direct current.
Normally, the gain at very low frequency is mea-
sured and considered as the gain of direct cur-
rent. By contraries, having no effect of DC offset
will be an advantage.
•Cannot measure spectrum
FRAs have a characteristic of being not suscepti-
ble to disturbance noise. In other words, frequen-
cy component that is different from the frequency
of internal oscillator will be hardly detected when
input. Therefore, FRAs cannot measure spectrum.
6. What cannot be done with FRA?
The methods and systems to measure frequency
responses were previously described. The frequen-
cy range of these measuring instruments is ex-
pressed schematically on the right.
7. Frequency range of measuring instruments
t
t
t
t
Level
Frequency
Level
Frequency
Level
Frequency
Level
Frequency
Level
Frequency
Level
Frequency
DUT
DUT
First Measurement
Second Network Analyzer
Oscillator + AC Voltmeter
FRA
FFT
Dynamic
Range
Measured Frequency Range
Oscillator+ AC Voltmeter
Frequency Response Analyzer
FRA
FFT Analyzer
+ Signal Source
Network
Analyzer
GHz
MHz
kHz
Hz
mHz
DC
100dB
3 Mechanism of FRAs (Frequency Response Analyzers)
2.1 Signal source
The (internal) signal source used for measurement
in FRAs is the sine wave of a single frequency that
has a line spectrum. In a single measurement, only
the gain and phase of the single frequency is ob-
tained. On the other hand, FFTs use a signal source
that has wide frequency spectrum such as random
noise and impulse for measurement to measure
frequency response of wide range of frequency in a
single measurement.
Although random noise signal may seem to
be better than sine wave, sine wave that contains
only a single frequency is overwhelmingly superior
in actual measurement. Here are the reasons.
To measure frequency response, a signal (ei-
ther sine wave or random noise) is to be applied on
the device under test. The signal applied at this
point must be the size that does not saturate the
DUT. For example, applying a signal of 1 V or more
as the input to an amplifier that can handle only up
to 1 V will saturate the amplifier and measurements
cannot be performed correctly. The waveform and
amplitude spectrum of random noise (typical signal
source used in FFTs) which amplitude is 1 V at its
peak, and those of sine wave are shown below.
The difference between FRAs and FFT analyzers or
network analyzers is that there are a DC elimination
circuit and a noise-eliminating LPF as well as a vari-
able gain amplifier between input terminals for anal-
ysis (CH1 and CH2) and A/D converter. After these
analogue preprocessing, the input signal is digi-
tized by the A/D converter. Then, with DFT opera-
tion, gain and phase are calculated and a graph is
displayed.
The mechanism and the principle of operation of FRAs are shown below.
1. FRA block diagram
This section describes internal structure of FRAs and functions specific to FRAs.
* FRA refers to FRA5095/FRA5096 unless specified otherwise.
2. Overview and functions of each section
AMP
CH1
CH2
OSC
LPF
Eliminates
DC
Analyzing Section CH1
Same as CH1
Analyzing Section CH2
Internal Oscillator
Display
DFT
Operation
A/D
A/D
D/A
Level
−1.2
−1.0
−0.8
−0.6
−0.4
−0.2
0.8
0.6
0.4
0.2
0.0
1.0
1.2
Time
Waveform
0.0
0.2
0.4
0.6
0.8
1.0
Frequency
Spectrum
Amplitude
Random Noise (Used in FFTs)
4 5

5. The table above shows that only a eightieth signal
of the random noise is necessary to obtain the
same measurement S/N ratio when using sine
wave. To put this in another terms, sine wave will
have 80 times ( 38 dB ) better S/N ratio than
random noise when the measurement signal of the
same size (peak) is used.
Even with random noise, by averaging 6,400
times (= 802), the S/N ratio will be the same as that
of sine wave and the frequency data of 1,024
points will be obtained. However, when using sine
wave, the measurement data for 6,400 points can
be obtained in the same measurement time.
The oscillator built in FRAs has the charac-
teristics such as
•Same frequency precision as quartz oscillator
•Resolution of 10 µHz in the entire frequency
range (FRA5096: 10 µHz to 15 MHz)
•Good phase-noise characteristic
•Frequency can be changed instantaneously in
continuous phase
due to DDS (Digital Direct Synthesis Method).
This is an oscillation method favorable to FRAs that
need to sweep frequency. In addition, using sine
wave for measurement allows measurement to be
completed quickly with good S/N ratio.
2.2 Input coupling
Analyzers that can measure low frequency such as
oscilloscopes and FFT analyzers are almost always
capable of switching input coupling between
AC/DC. This is to detect small AC signals (mea-
surement signals) superposed on direct current.
General input coupling circuit of analyzers is shown
on the right.
With FFTs, frequency response is calculated from
the change of spectrum distribution that is given
only at quite low level compared to its full scale. On
the other hand, with FRAs, frequency response is
calculated from the signal that has the spectrum of
around the same size as its full scale (sine wave).
Although it is evident which is superior considering
measurement precision and S/N ratio, let's make
more quantitative comparisons.
Sine Wave (Used in FRAs)
Level
−1.2
−1.0
−0.8
−0.6
−0.4
−0.2
0.8
0.6
0.4
0.2
0.0
1.0
1.2
Time
Waveform
0.0
0.2
0.4
0.6
0.8
1.0
Frequency
Spectrum
Amplitude
Peak
Random Noise Sine Wave
1 Vpk 1 Vpk
1 Around 80
0.286 Vrms
8.94 mVrms
(2,048 Points FFT)
0.707 Vrms
0.707 z
RMS
Spectrum Level Percentage
Spectrum Level
Input Coupling Changing Switch
Input
DC
C
R
AC
2.3 Auto ranging
One of the characteristics of FRAs is the auto rang-
ing with which measurement range is changed ap-
propriately during sweep measurement. With other
analyzers (such as FFTs or Network Analyzers), the
measurement range is fixed to a preset value.
The auto ranging of FRAs is similar to the
measurement procedure for “Oscillator + AC Volt-
meter”. If the reading of the AC Voltmeter is too low
(meter needle does not move too much), you need
to lower the measurement range (increase sensitivi-
ty) so that the meter needle moves as much as
possible. On the contrary, if the meter needle ex-
ceeds the full scale, you need to raise the mea-
surement range (decrease sensitivity) so that the
needle remains within the full scale and then per-
form measurement again. FRAs perform auto rang-
ing automatically in the same way during sweep
measurement and always set the system to the op-
timum range ( not too high, not too low ) before
measurement.
Capacitor C cuts the portion for the direct current.
However, the signal from low frequency of a few Hz
or less attenuates along with the signal from direct
current and this produces error at low frequency.
Also taking phase into consideration, we have no
choice but to measure frequency of tens of Hz and
lower with DC coupling. If DC current is super-
posed on for a great amount as is the case with
servo characteristic measurement, measurement
range must be wider and the measurement result
will be given only with poor S/N ratio. In addition, if
the input direct current changes suddenly, it takes
a bit before the direct current level is settled at zero
(canceled) (there are some transient responses).
Although FRAs can measure infrasonic fre-
quency of mHz order or less, input is always in DC
coupling. The portion for direct current is eliminated
not by AC coupling but by offset cancel circuit
shown on the right.
DFT operation section detects DC compo-
nent as well as calculates gain and phase to con-
trol D/A converter so that DC portion will be zero.
Compared to DC elimination with general AC cou-
pling, this DC elimination has characteristics as de-
scribed below.
•DC portion is eliminated instantaneously, and there
is no transient response.
•DC portion can be eliminated with no change in
amplitude and phase even at infrasonic frequency.
Input
From
DFT Operation Section
D/A
Set Oscillator Frequency
Set Oscillator Frequency
Set Oscillator Frequency
Up
Range
Down
Range
Up
Range
Down
Range
Measurement
Measurement
Ranging When Measuring with AC Voltmeter
6 7

6. By detecting the phase of CH1 and CH2 input
signal to calculate amplitude V and phase θ, ratio
(gain) and phase difference between the channels
are calculated. All of these operations are done by
CPU software. Computing done at each channel is
almost the same as 2-phase type digital lock-in
amplifiers .
Phase detection is a technique to convert the fre-
quency of the measured signal into direct current
by using heterodyne that is better known in radio
circuit issues. FRAs use the internal oscillator as
multiplying signal for heterodyne and detect the fre-
quency component that is equivalent to this multi-
plying signal (= internal oscillator). Among the vari-
ous signals that the measured signal contains ,
only the phase of the component that is equivalent
to the frequency of the internal oscillator is detect-
ed and converted into direct current. Other compo-
nents are converted into AC signals that frequency
is not equal to 0 and thus, eliminated in averaging
block. Averaging process behaves like LPFs.
This operation in the frequency area can be
described as shown in the figure below.
2.4 DFT operation
FRAs calculate gain and phase with DFT operation.
The block diagram for DFT operation is shown
below.
Phase Detection
sin(ωt)
CH1
CH2
+90°
θ1− θ2
X2
+Y2
Y
X
V1
V2
tan−1
Averaging
Averaging
Gain
Phase Difference
X
V1
V2
θ1
θ2
Y
Signal
Noise
Folded back with
Direct Current
Spectrum of Measured Signal
Spectrum of Internal Oscillator
Spectrum of Multiplier Output
Spectrum of Averaging Output
Equivalently
f
fm
f
fm
f
f
2fm
0
(DC)
f
fosc
2.5 Integrals and S/N
DFT operation averages the phase detection output
by the cycle of the frequency to be analyzed. “Aver-
aging” section in the DFT operation block diagram
(P.8) corresponds to this. FRAs set this averaging
unit (the number of cycles) by using “integral count”.
Because FRAs average (integrate) outputs by the
cycle, it essentially has the function to eliminate
noise and harmonic waves.
If noise is great or measurement with high
precision is required, measurement can be conduct-
ed with higher precision by increasing integral count.
Random noise decreases almost in proportion to the
square root of the integral count. The integrating
effect is shown below. This is an example in which
damping characteristic of LPF is measured. You can
see that by increasing the integral count by 100 from
1 to 100, the noise level improved to about 20 dB
(10 times lower).
This integral setting corresponds to averaging in FFT
analyzers, and RBW (resolution bandwidth) setting
in network analyzers.
2.6 Delayed measurement
When the frequency of the internal oscillator is
switched (while sweeping), measurement data will
involve error due to transient responses if the DUT
has answer delay. To minimize this error in FRAs,
you can set any value as the time from the change
of frequency to start of the measurement. This is an
essential setting item for vibration test that shows
sharp resonance and for measuring resonant
device.
−120
−100
−80
−60
−40
−20
0
100 1k 10k 100k
One Integral
Hundred Integrals
Frequency [Hz]
Integrating Effect
Gain
[
dB
]
OSC Output Waveform
OSC Frequency = f1 f2
DUT Response Waveform
Measured Waveform Range with
Appropriate Delay
Measured Waveform Range with No Delay
Time
Response Waveform That Needs Delayed Measurement
8 9

7. 2.7 Amplitude Compression
To prevent DUT system from saturating or being
damaged when amplitude response of the DUT
system has a great peak, ALC (Automatic Level
Control) function controls the output level of the
oscillator so that the amplitude level of the DUT
system remains constant. In FRAs, this function is
called Amplitude Compression.
2.8 Frequency axis slow speed high density sweep
Normally, FRAs perform frequency sweep at regular
intervals (linear or logarithmic) between the lowest
frequency and the highest frequency being set. If
characteristic changes drastically such as a sharp
peak in frequency response, greater amount of
measurement data needs to be obtained by
increasing sweep density. However, if there are sec-
tions where characteristic changes drastically and
sections where characteristic is smooth, even the
smooth sections will be measured at density higher
than necessary and this will increase the measure-
ment time and data for nothing.
In FRAs, frequency axis low speed high den-
sity sweep (Slow Sweep) automatically adjusts
sweep density to be high for sections where char-
acteristic changes drastically, and low for smooth
sections so that more precise data can be obtained
in short period of time. You can set the value that
should be considered as drastic change as you like.
The figure below is an example in which the
impedance characteristic of 1 MHz quartz oscillator
was measured with FRA with Slow Sweep Function
ON. The •s in the graph indicates the position of the
measured data (thinned at intervals). You can see that
the sections where characteristic drastically changes
such as peak and dip are measured densely.
A typical application example of this amplitude
compression is vibration test. With this function,
reference acceleration pickup can detect the char-
acteristic of vibration tester (shaker) and control
amplitude while constant acceleration is being ap-
plied on the sample regardless of frequency.
The figure below shows a measurement ex-
ample for evaluating anti-vibration characteristic of
the vibration-proof material.
SUT
f
Gain
OSC CH1
CH2
FRA
FRA
This Amplitude to Be Constant
Charge Amplifier
Vibration-
Proof Material
Measuring Pickup
(Reference)
Acceleration
Pickup
Shaker
Power
Amplifier
CH1
CH2
|
Z|
[Ω]
Frequency [kHz] Ref =1 MHz
−1.2 −1.0 −0.8 −0.6 −0.4 −0.2 +0.0 +0.2 +0.4 +0.6 +0.8 +1.0 +1.2
2.9 I/O isolation
When signals are injected serially into a circuit as is
the case with servo loop measurement, a signal
source (oscillator) that is isolated from ground is
required. In addition, if the reference potential is dif-
ferent from ground potential, the input to the analyz-
ing section needs to be isolated from oscillator,
other inputs to be analyzed, and casing (chassis
ground). Measurement examples in which inputs to
be analyzed and oscillator need to be isolated are
shown below.
Depending on FRA models, isolation voltage and
maximum measurement voltage of each terminal is
restricted as shown below. Be careful not to apply
high voltage that exceeds specification on FRA.
OUTPUT
CH1
CH2
OSC
CH2
DUT CH1
OSC
Rs
Z = V(CH1) / V(CH2)
v
i
●Servo Loop Measurement of
Switching Power Supply
To Error
Amplifier
*OSC needs to be isolated
●Impedance Measurement of
A Capacitor
*CH2 needs to be isolated
CH2
CH1
OSC
Vcc
hfe = V(CH1) / V(CH2)
DUT
ib
ic
●hfe Measurement of A Transistor
*CH1 and CH2 needs to be isolated
Section for Inputs to Be Analyzed
Oscillation Section
Model Name
Maximum Input Voltage
Isolation Voltage
Isolation Voltage
FRA51602/FRA51615
FRA5087/FRA5097
FRA5022/FRA5014
5055*
600 Vrms CAT Ⅱ
300 Vrms CAT Ⅲ
600 Vrms CAT Ⅱ
300 Vrms CAT Ⅲ
±10 V
±11 V
±11 V
250 Vrms
30 Vrms
250 Vrms
600 Vrms CAT Ⅱ
300 Vrms CAT Ⅲ
±11 V
30 Vrms
250 Vrms
* 5055 is not a FRA but a signal injector probe that is to be used together with FRA.
10 11

8. 4 Measurement Example Using FRA
1. Gain-phase measurement example
FRAs are mainly used for the following three pur-
poses: (1) Gain-phase measurement, (2) Imped-
ance measurement, and (3) Servo characteristic
measurement. Various typical applications using
FRA5095/FRA5096 and measurement tips (such
as how to reduce errors) are given here.
As examples of measuring gain-phase, the follow-
ing three are described here with actual measure-
ment examples.
•Frequency response measurement of filter
•CMRR measurement of differential amplifier
•Damping (Transfer) characteristic measurement
of power line
How to reduce measurement errors in
gain-phase measurement is described at the end as
well.
The following two points are what you should pay
attention to during measurement.
•Use the cables of the same type and size for two
cables between CH1 and SUT, and CH2 and SUT.
•The input signal for CH2 shall be obtained from
SUT input.
Using damaged cables or connectors with
poor contact will cause measurement errors. The
error of around 0.03 dB will be easily yielded
although it varies depending on the conditions.
Frequency response measurement of filter
Gain
Phase
Gain×100
Gain
[
dB
]
Phase
[
deg
]
Frequency [Hz]
FRA
SUT out
in
T-Branch
BNC Connector Cables of same
type and size
SUT
V2 V1
A
−100
−80
−60
−40
−20
0
20
−180
−120
−60
0
60
120
180
10 100 1k 10k 100k
Connections Circuit under Test
Measurement Example
The capacity of differential amplifiers to eliminate
common mode noise (Common Mode Rejection
Ratio ) usually shows a great value of 60 dB or
more. An analyzer with a great dynamic range is
required to measure CMRR of differential amplifiers.
This is a good application example that makes
good use of FRA performance.
The wiring for differential amplifier (SUT) input shall
be as short as possible while loop area shall be as
small as possible as well to prevent noise of exter-
nal magnetic field, etc. from mixing in.
Connections Circuit under Test
Measurement Example
CMRR
[
dB
]
BEST BETTER
*CMRR = Common Mode Gain [dB] − Differential Gain [dB]
Frequency [Hz]
FRA
SUT
in out
SUT
in out
FRA
FRA
SUT
in+
out
in−
GND
Short wiring
SUT
V2 V1
A
0
20
40
60
80
100
120
140
160
10 100 1k 10k 100k 1M
CMRR measurement of differential amplifier
12 13

9. There are following two methods to reduce errors
in the measurement of gain-phase characteristic.
(1) Pay attention to measurement cables
In general, a coaxial cable (such as 3D-2V or
RG-58A/u) is used as the cable to connect FRA
and SUT.
These 50 Ω coaxial cables have;
•Capacitance of 100 pF/m
With signal source resistance of 100 Ω, error
is −0.017 dB and −3.6 deg (at 1 MHz).
•Propagation delay time of 5 ns/m
Error of −1.8 deg at 1 MHz
As described in the example of measuring filter
characteristic, using the same cable for CH1
and CH2 will offset these errors.
(2) Use equalizing function
FRAs are equipped with a function to normalize
the pre-measured characteristic to the standard
value (0 dB and 0 deg) (Equalizing Function).
Using this function allows you to offset the
errors in the system of measurement such as
measurement cables, probes, and external am-
plifiers so that the characteristic of the SUT
alone can be calculated simply.
Tips to reduce errors
How to use equalizing function
•Remove SUT and connect (short) input/output to
conduct sweep measurement.
•Store the measurement result in the equalize memory.
step-1 Measure errors in the system of measurement.
step-2 Turn on equalizing function and
conduct measurement.
•Turn on the equalizing function.
•Connect SUT and conduct sweep measurement.
↓
With the error in the system of measurement being
offset, the frequency response can be measured.
FRA
Amplifier
Probe
FRA
Amplifier
Probe
SUT
out
in
2. Impedance measurement example
Besides gain-phase measurement described in the
previous section (p.13 − ), the measurement of im-
pedance characteristic is also a main application of
FRA.
By measuring and dividing voltage and cur-
rent components of inputs to be analyzed at 2
channels of FRA, the absolute impedance and
phase (complex impedance) can be calculated.
Normally, LCR meter, which is an exclusive
measuring instrument, is used for measuring im-
pedance. The comparison between using LCR
meter and FRA for measuring impedance is given
in the table below.
Test Voltage and Current
LCR Meter FRA
Small Great degree of freedom
Fixed
(External Factor)
Variable
Measurement Accuracy
Circuit under Test
Although an example with an electrolytic capacitor
is given, the measurement shall be the same for
other electronic parts. Because the internal oscilla-
tor of FRAs allows you to set DC bias as well, mea-
surement can be conducted with FRA alone if the
voltage is 10 V or less.
Current is detected with current-detecting resistor
(shunt resistor) of approximately 1 Ω.
When measuring with further greater voltage
and current, the OSC output of FRA shall be ampli-
fied with an external amplifier. With our High Speed
Bipolar Power Amplifier HSA series, the output can
be amplified up to 300 Vp-p. A current probe (CT)
shall be used for detecting current when high cur-
rent is to run through the sample.
By using the optional impedance measure-
ment adapter, four-terminal measurement can be
conducted easily with FRA unit alone (see P.21:
Tips to reduce errors) .
Although the measurement accuracy of LCR is far
better than that of FRA, the greatest advantage of
conducting impedance measurement with FRA is
that test voltage or current can be set to the value
you desire. By amplifying the output signal of oscil-
lator with an amplifier, voltage up to 250 Vrms can
be applied on a sample. If you use a current probe
(CT), test current can be even tens of amperes and
higher.
As an example of measuring impedance with
FRAs, the followings are described with actual
measurement examples.
•Impedance characteristic measurement of
electrolytic capacitor
•Output impedance measurement of switching
power supply
•Impedance measurement of power line (interior
wiring)
•Impedance measurement of quartz oscillator
How to reduce measurement errors that are
specific to impedance characteristic measurement
is described at the end as well.
Impedance measurement of electrolytic capacitor
Connections
Measurement Example
|
Z
|
[
Ω
]
Frequency [Hz]
FRA
Electrolytic Capacitor
under Test Current-Detecting
Resistor
1m
0.01
0.1
0
10
100
1k
10k
100k
100 1k 10k 100k 1M 10M
Ceramic capacitor 0.01 μF
Film capacitor 40 μF
Electrolytic capacitor 100 μF
14 15

10. Most of time, load regulation is defined in the spec-
ification of switching power supply. Load regulation
is the voltage drop with no load and with rated
load, and is a value caused by output (DC) resis-
tance. Although this is valid for DC type load, it will
be of no help when load current changes. Needless
to say, DC voltage is being output to the switching
power supply in operation, and output impedance
cannot be measured with LCR meter. However,
with FRAs, output impedance may be measured in
simple configuration. Output impedance can be
measured with the switching power supply alone,
as well as with some load connected.
The current-limiting resistor in the connection dia-
gram limits the adverse current from the output of
the switching power supply to the OSC (output
impedance of 50 Ω) of FRA. The resistance is de-
termined so that the adverse inrush current will be
around 2 to 30 mA or lower.
For example, if the output of a switching
power supply is DC24V, the current-limiting resis-
tance shall be approximately 2 kΩ (adverse inrush
current of around 12 mA).
The result of measurement with FRAs is given
by voltage/current gain (dB). While actual imped-
ance needs to be corrected using current-detecting
resistor, current-detecting resistor of 1 Ω requires
no conversion and is very convenient since it is an
appropriate resistance for this measurement.
Output impedance measurement of switching power supply
Connections
Measurement Example
|
Z
|
[
Ω
]
Phase
[
deg
]
Frequency [Hz]
FRA
Switching Power
Supply under Test
Current-
Detecting
Resistor
Current-
Limiting
Resistor
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
−90
−70
−50
−30
−10
10
30
50
70
90
0.1 1 10 100 1k 10k
Phase
|Z|
High frequency sweep density and great dynamic
range are required for measuring impedance of the
parts with sharp resonance characteristic such as
quartz oscillators and piezoelectric actuators. With
various functions of FRA such as 10 µHz frequency
resolution for up to maximum test frequency
(FRA51615: 2.2 MHz), maximum of 20,000 sweep
frequency points, and slow sweep, impedance
characteristic of the devices on which measurement
is difficult (such as quartz oscillators) can be mea-
sured in short period of time with high accuracy.
Impedance measurement of quartz oscillator
Connections
Measurement Example
|
Z
|
[
Ω
]
∆Frequency [Hz] Ref = 1 MHz
Phase
[
deg
]
FRA
Quartz Oscillator
under Test
Current-Detecting
Resistor
100
1k
10k
100k
1M
10M
−100
−60
−20
20
60
100
5 4 3 2 1 0 −1 −2 −3 −4 −5
Phase
|Z|
16 17

11. To reduce errors in impedance measurement, you
need to pay attention when creating jigs such as
wiring cables with the shortest route and wiring
with four-terminal method. Wiring with two-terminal
method will cause unnecessary impedance to be
measured. Especially, measuring a device of low
impedance calls for attention.
In gain-phase measurement, errors in the system of
measurement are corrected by equalizing function.
In impedance measurement, errors are corrected
with short correction/open correction.
(1) Short correction ... When measuring a device
of low impedance (about 10 Ω or lower)
(2) Open correction ... When measuring a device
of high impedance (about 1 kΩ or higher)
When the impedance of the DUT changes
greatly, conducting both of short correction and
open correction is of course effective. There will be
no great difference no matter which correction is
made first.
For these corrections, operations can be
made automatically when optional Impedance Dis-
play Function (PA-001-341) is added.
Tips to reduce errors
FRA
DUT
DUT
DUT
Voltage
Detection
 To CH1
Voltage
Detection
 To CH1
DUT
Measurement with Two-Terminal Method
Measurement with Four-Terminal Method
FRA
Voltage-Detecting
Resistor
3. Servo measurement example
Disc systems such as CD and HDD, switching
power supplies, and robots demonstrate their per-
formance with sophisticated auto control (servo
loop).
While servo loop demonstrates great works if
designed and implemented properly, they do not
only fail to demonstrate their proper performance,
but also involve danger when designed improperly.
Measuring servo loop characteristic allows you to
obtain the following characteristics.
(1) Steady-state error characteristic
The greater the gain at direct current (low fre-
quency close to direct current) is, the better this
characteristic should be. Let's take an example
of a switching power supply. No matter how
great the accuracy of the reference power
supply may be, the resulting accuracy will be
lower if the gain is small.
(2) Stability
This is the most interesting issue in loop char-
acteristic measurement. You can judge this
from phase margin or gain margin. With stability
being insufficient, overshooting may take place,
or in the worst case, the loop oscillates and this
makes control impossible. Even if it seems
stable, measuring loop characteristic may
reveal the fact that it was just at the limit before
oscillating.
(3) Tracking
The outline of the control volume tracking to
reference value can be determined with the fre-
quency at which the gain of the finish charac-
teristic (closed loop characteristic) starts to de-
crease.
Servo loop characteristic is also called “Loop Char-
acteristic” . Roughly, there are the following two
methods to measure loop characteristic.
With either method, loop characteristic Aβ
can be measured by using e1/e2. However, method
1 is not realistic because output e0 will greatly fluc-
tuate with a fine adjustment of Vbias being slightly
inappropriate. For example, with loop gain of 60 dB
( 1000 times ), 1 mV of fluctuation in Vbias will
change e0 by 1 V, and most of time, this will satu-
rate the circuit.
With method 2, although measurement
signal source Vac needs to be floating from the
ground, Vbias is not necessary. In servo characteris-
tic measurement, method 2 in which the character-
istic can be measured. with the circuit actually in
operation is used.
While loop characteristic (Aβ) measurement
with method 1 is intuitive, loop characteristic Aβ is
calculated from eg which is the disturbance signal
injected into the loop when method 2 is used.
The reason why loop characteristic Aβ can
be measured with method 2 is given below.
•eg = Constant
•eg = e2 - e1
From connection diagram, these relations are obvi-
ous. Using them, loop characteristic (board dia-
gram) and the relations among eg, e1, and e2 at
each frequency are illustrated with vectors on the
next page.
Method 1 Method 2
β
ei
e1
e0
A
A
eg
vbias
e2
e2
ei
e1
e0
β
eg
+
−
+
−
18 19

12. ei
β
e0
A
eg
eg
e2
180°
e2
e2
e2
e2
e2
e1
e1
e1
e1
e1
e1
90°
0°
0dB
eg
eg
eg
eg
1
2
3
4
(Oscillating)
Gain = e1/e2
Frequency
Phase
+
−
+
|e1|=|e2|
|eg| : Constant
eg = e2 − e1
1 2 3
4
: At low frequency close to direct current, e1 and
e2 have opposite phases (negative feedback),
and thus, |e2|<
<|e1|.
: In the area where gain attenuates at the rate of
6 dB/oct, the phase difference between e1 and
e2 is 90 degrees.
: At frequency where gain is 0 dB, |e1| = |e2|.
The angle difference between e1 and e2 at this
point is called “Phase Margin” . The greater the
phase margin is, more stable the circuit is.
: When the gain becomes negative and phase
difference gets closer to 0 degree as the fre-
quency increases, e1 gets smaller.
The conditions for loop oscillation are that the loop
characteristic has (1) gain of 0 dB (×1), and (2) the
phase difference of 0 degree (or multiplier of 360
degree). At frequency that satisfies these two con-
ditions, e1 and e2 are infinite for eg of finite size as
shown in the vector diagram in the figure above
( oscillating ). This means, e1 and e2 are always
present even if eg becomes 0, and a signal of con-
stant frequency will be always present in the loop
even if the signal source eg is removed. In other
words, oscillation continues.
Note that oscillation will not take place even
if the phase difference is 0 degree if the gain is not
0 dB. The gain with the phase difference of 0
degree is called “Gain Margin” . The vector relation
with positive gain margin is shown in the figure on
the right.
The smaller the gain margin is, the greater e1
and e2 will be for the disturbance eg of the same
size. This means that even if the gain margin is 6
dB, e1 will be the double size of eg, and thus, great
ringing and overshooting will be taking place.
So far, we have injected disturbance signal eg on β
side. Although you can inject disturbance signal at
wherever in the loop to measure loop characteris-
tic, in actual negative feedback circuits, the distur-
bance injected on A side will be suppressed with
influence of negative feedback. The greater the
gain is, the smaller the influence of the disturbance
injected to the output (or input) of A side (e2) on
output e0 will be.
2
3
4
1
e2
e1
eg
e2
e1
eg
With Gain Margin of 6 dB
With Gain Margin >> 0 dB
FRAs are also effective to measure and evaluate
servo loop characteristics. Basically, servo loop can
be measured with a measuring instrument that can
measure transfer characteristic. However, in actual
servo loop measurement, high basic performance is
required. It is not too much to say that FRAs were
developed to achieve the tough basic performance
required in servo loop measurement. The followings
are the tough points in servo characteristic measure-
ment.
(1) Great gain at low frequency close to DC
The voltage on loop input side becomes extremely
low. Because the voltage on loop output side,
which is relatively great, must be measured simul-
taneously, a great dynamic range is required.
(2) Oscillator must be floating
For stable measurement with circuit actually in
operation, measurement signal (disturbance
signal) needs to be injected serially into the
loop. Therefore, the oscillator output of the ana-
lyzer is required to be floating.
(3) Measurement in wide frequency range
The measurement range from a few Hz and
lower that can be considered almost as DC
gain to tens of kHz is required. Because the fre-
quency ranges widely, frequency axis needs to
be graduated in logarithmic scale.
Some measurement examples of servo loop
characteristic using FRAs are given below. Points
to be kept in mind during measurement are de-
scribed together as well.
Measurement signal is injected between the output
terminal and the error amplifier. While an injection
resistance of a few tens of ohms is not necessary
for measurement, connection cable to the FRA
being disconnected improperly makes the circuit
open loop and thus, is dangerous. The injection
resistor is necessary also in terms of safety.
With a great dynamic range of FRAs, neat
data can be obtained even if the level of the inject-
ed signal is capability of FRAs to eliminate DC
signal, the gain of 1 Hz or lower can be measured
with a switching power supply actually in operation.
Loop gain measurement of switching power supply
Injection Resistor
(50 to 100Ω)
+
PWM
Vref
FRA
Switching Power Supply
Load
Error
Amplifier
Frequency [Hz]
Phase
Gain
Loop
Gain
[
dB
]
Phase
[
deg
]
0
90
180
270
360
450
540
−60
−40
−20
0
20
40
60
0.01 0.1 1 10 100 1k 10k 100k
Connections
Measurement Example
20 21

13. It is not rare, although it depends on the type, that the
DC open loop gain of an operational amplifier
exceeds 100 dB. Generally, measurement of open
loop gain is very difficult. However, gain characteristic
at low frequency can be measured relatively easily
with FRAs. Note that abnormal oscillation will take
place if careful attentions are not paid, such as
wiring in the shortest distance.
Open loop gain measurement of operational amplifier
Instead of using functions of FRAs, errors in the
servo characteristic measurement shall be reduced
by devising measurement method itself.
The followings are the typical ways to reduce
errors.
(1) Selection of injection and measurement point
(2) Use of signal injector probe
(3) Use of summing amplifier
(1) Selection of injection and measurement point
No matter where you make measurement in the
loop, you will be able, in theory, to obtain the
same loop characteristic. However, with new
time constant generated because of impedance
of the actual circuit and capacitance of FRAs or
signal cable, measurement errors will be yielded.
If this time constant can be sufficiently smaller
than the time constant of the circuit under test,
the measurement errors can be ignored.
The best location to interrupt the loop to
inject/measure signal is where the impedance of
upstream loop is low and the impedance of
downstream loop is high. With a switching
power supply shown in the figure on the next
page, the signal travels in clockwise direction as
shown with the arrow. A large electrolytic capac-
itor for eliminating noise keeps the impedance of
the output terminal low and an attenuator that is
an input for the error amplifier generally has im-
pedance of a few kW or higher, and thus, loop
characteristic can be measured at this point
without any problem. Injection resistance R2
must be sufficiently smaller than R1 (generally
around a few tens of ohms), or the output volt-
age will fluctuate.
Tips to reduce errors
Connections
Measurement Example
R2<<R1
FRA
DUT
+
R1 R2
Switching Power Supply
Error
Amplifier
Upstream Loop
(Signal Source Side)
Downstream Loop
(Load Side)
+
−
PWM
Load
High
Impedance
Low
Impedance
Gain
[
dB
]
Frequency [Hz]
Phase
[
deg
]
Phase
Gain
−20
0
20
40
60
80
100
120
140
−90
−45
0
45
90
135
180
225
270
1 10 100 1k 10k 100k 1M
(2) Use of signal injector probe
Time constant generated during loop character-
istic measurement with FRA is caused by the
following factors (floating capacitance).
•Input capacitance at FRA analyzing section
≈ 20 pF × 2 ch
•Floating capacitance at FRA oscillating section
≈ 250 pF
•Cable capacitance ≈ 100 pF × 2 + ?
They total over around 500 pF. If the
impedance (for resistance) at the upstream of the
loop is around 100 Ω, a pole is generated at fre-
quency of 3.2 MHz. This creates change in the
phase characteristic at frequency of around 320
kHz. With greater impedance at the upstream of
the loop, the change appears at lower frequency.
These floating capacitance generated in
FRA alone can be reduced to around 50 pF if
Signal Injector Probe 5055 is used. By placing
5055 near the circuit under test and connecting
it in the short distance allows you to reduce the
influence of floating capacitance.
The power for 5055 is supplied from the
FRA. All the models of our FRAs are equipped
with power connector for 5055 and thus, no
separate DC power supply is required.
Note that while using 5055 allows you to
reduce the influence of errors, the maximum
test frequency is limited to 100 kHz and the
maximum voltage to ±11 V.
Connection Diagram for Servo Measurement with 5055
Signal Injector Probe 5055
(3) Use of summing amplifier
Using Signal Injector Probe 5055 can greatly
reduce errors. Although errors can be reduced
to be sufficiently low to be ignored in most servo
measurements, errors may not be able to be
ignored even by using 5055, depending on the
(impedance of) circuit.
In that case, also use a circuit for sum-
ming and detecting amplifier shown within the
dotted line in the figure below. The operational
amplifier shall have GB product that does not
affect the characteristic of the circuit under test.
The input impedance R1 + R2 at the summing
amplifier section shall be sufficiently smaller than
the output impedance Zout so that the time
constant conditions are the same as the original
setting with no summing amplifier.
PWM
Vref
FRA
+
Switching Power Supply
Error
Amplifier
Connect in the Short Distance
Zout
eg
R1
R2
R1+R2
+
−
−
+
−
+
r
β
e1
e2
r
r
r
r
Summing and Detecting Amplifier
5055
A
+
Load
(CH1, CH2) (OSC)
22 23

14. 5 Q & A
Which one of open correction or short
correction shall be used for measuring the
impedance of a capacitor?
If the capacitance of the capacitor to be
measured is great, short correction shall be
used. Vice versa, if the capacitance of the
capacitor to be measured is small, open
correction is appropriate.
While there is no clear definition on at
which capacitance the appropriate correction
shall change, around a few 100 pF shall be the
reference of switching from/to short correction
to/from open correction, considering the
floating capacitance of measurement cables
and FRAs. Of course, both of open correction
and short correction may be applied to the
same sample. In this case, perform short
correction on the characteristic which open
correction was done ( there will be no big
difference even if short correction was done
before open correction).
May I consider that DC-type gain cannot be
measured with FRAs?
Yes. FRAs cannot measure DC gain. While they
cannot measure real DC, they measure the
gain at frequency sufficiently low to be
considered as DC and judge the result as DC
gain. Because of the influence of offset voltage
and temperature drift, it is very difficult to
precisely measure real DC gain. By measuring
gain at very low frequency, precise gain can be
measured with no effect of offset voltage and
drift.
Can I capture data measured with FRA51615 /
FRA51602 into PC as Excel data?
Yes, you can. FRA data is in binary format and
thus, cannot be directly loaded with Excel.
However, by using the software attached to the
product of standard specification, you can
display a graph and save the data in text
format (csv format).
Can I make the hardcopy of the measurement
result with FRA1615 / FRA51602?
You can, if your system is equipped with
firmware of Ver.2.xx. If your firmware is in
ver.1.xx, we upgrade your firmware for free.
A
Q How can I measure the loop characteristic of a
switching power supply that has constant
current output?
G e n e r a l m e t h o d t o m e a s u re t h e l o o p
characteristic of a switching power supply with
constant current output is to use a shunt
resistor to convert the output current into
voltage and to feedback the voltage to the
error amplifier. Because the shunt resistance is
as low as a few ohms or less, injecting
/detecting signal between the shunt resistor
and the error amplifier allows you to conduct
measurement without any problem.
Can I correct the phase characteristic in
impedance measurement?
Phases are corrected automatically along with
impedance during open or short correction
(corrected with a set of Z and 0 ). Therefore, no
correction for phase characteristic alone is
required.
How much resistance is appropriate for
current-detecting resistor in impedance
measurement?
While there is no distinct standard, followings
shall serve as reference.
•Minute current (around a few mA and
lower): around 10 Ω to 1 kΩ
•Low to medium current (around a few
hundreds of mA or lower): around 1 Ω
•High current (a few A and higher):
Use CT or current probe
In general, a current-detecting resistor that has
a value close to the impedance of the object to
be measured is appropriate . However, you
need to be careful of the frequency response
the resistor has. Wirewound resistors and
resistors with great resistance over kΩ scale
are not appropriate. With carbon/metal film
resistors or solid resistors, the resistance shall
be determined within the range of 1 Ω to 1 kΩ.
A
Q
A
Q
A
Q
A
Q
A
Q
A
Q
Frequency Response Analyzer
Technical Guide
The contents of this technical guide are current as of June, 2020
Measurement Principle and How to Measure Various Frequency Responses
Copyright© 2020 NF Corporation. All rights reserved.
6-3-14 Tsunashima Higashi, Kohoku-ku, Yokohama 223-0052, Japan
Phone: +81-45-777-7604
24

15. Frequency Response Analyzer Technical Guide
Measurement Principle and How to
Measure Various Frequency Response
NF Techno Commerce Co., Ltd.
6-3-14 Tsunashima Higashi, Kohoku-ku, Yokohama 223-0052, Japan
Phone : +81-45-777-7604 Fax : +81-45-777-7605
International Sales Division