# Instrumentation & Measurement Magazine 23-2 - 14

```Fig. 1. Typical spectrum amplitude. (a) A rectangular base-band pulse signal; (b) A pulse-modulated RF signal.

sampling oscilloscope (DSO) can be used. The method is useful for base-band pulse generators, since it is simple and
time-efficient. Corrections for the cable (attenuator) properties and oscilloscope transfer function must be performed.
A DRTO triggers directly the measured pulse. The traceability of DRTO is complicated due to the nonlinear behaviour of
modern analog-to-digital converters and the transfer function
correction. A DSO needs an external trigger signal, which is
usually derived from the measured signal itself (approx. 20 ns
delay line is used). The measurement is traceable to the electrooptic sampling system. A general diagram of the measurement
setup using the DRTO and DSO is shown in Fig. 3.
The measurement equation is the following:

6
 V ( f ) 2 ⋅ 10 ⋅ k ATT ⋅ kosc
S ( f ) = 20 log 
Δf

N FFT
106




 [dBμV/MHz],	(1)



where V(f) is the Fourier transform of the voltage trace from
oscilloscope in V; NFFT is the FFT length; Δf is the frequency resolution in Hz; kATT is the total attenuation of the signal path,

that is, the cables and external attenuators connected between
the generator and oscilloscope; and kosc is a factor taking into
account the oscilloscope frequency response. A cable with attenuators on both sides should be used to reduce the pulse
amplitude and improve the mismatch uncertainty.
The following text shows an example of measured and calculated results. The spectrum amplitude was calculated using
(1) from oscilloscope voltage samples corrected for the cable
and attenuator and oscilloscope transfer function. The following uncertainty contributions apply:
◗◗ impedance mismatch correction between device 1 and 2
(between a generator and cable) uM = 20 log 1 + Γ1 Γ 2
and
where
u20
= 201log
Γ Γ 2 are magnitudes of reflection coefuM =dB,
log
+ Γ11 +Γ
M
2 1
ficients of devices 1 and 2 (in linear scale), respectively,
◗◗ type A uncertainty was calculated from repeated calculations of the spectrum amplitude for all captured time
traces, and its value was determined from n measurements in a standard way.
The output reflection coefficient of the IGUU 2916 Main
generator is not specified in the datasheet [11], and it was calculated from a hypothetical generator composed of an ideal

( (

) )

(

)

Table 1 - Quantities used for characterization of pulse generators
Quantity

Definition

Notes
V(f) is the Fourier transform of the v(t) signal in the time-domain [9], [10]. It is the measure
of the amplitude spectrum at a certain frequency, expressed in dBμV/MHz. For a
rectangular pulse with amplitude A and duration T and low frequencies (f << T), we can
write S(f) = 2AT.

Spectrum
amplitude

S
​ ( f ) = 2 V ( f )​

Impulse
area

Aimp =  v ( t ) dt
​
​
0

Voltage-time area of a pulse defined by the integral. Sometimes referred to as impulse
strength, typically expressed in μVs or dBμVs. Related to spectral density. T is one pulse
period.

Spectral
intensity

S
​ ( f ) = 2 Aimp​

This definition can be found in [5] and [10].

Spectral
density

Defined in [5]. Alternative term "impulse strength" can be found. The term √2 stands for the
6
D
​ = 2 × 10 Aimp​ peak to RMS conversion. D is calculated in μV/MHz for Aimp given in μVs.

14

T

IEEE Instrumentation & Measurement Magazine

April 2020

```

# Instrumentation & Measurement Magazine 23-2

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