# Expanding the frequency range of a vector network analyzer.

Expanding the Frequency Range of a Vector Network Analyzer

The measuring of amplitude and phase vs. frequency characteristics of networks and systems is a common procedure for circuit performance characterization. Vector network analyzers (VNAs) are used widely for these measurements.

The basic setup for measuring the complex response of a device, using a VNA, is shown in Figures 1a and 1b for transmission and reflection characterization, respectively.

Sometimes there is a need to measure the frequency response of a device at higher frequencies than the upper bandwidth limit of the network analyzer available. This paper presents a method to deal with this situation. The method has been applied to a particular case in which the HP 3575A network analyzer, with a working bandwidth up to 13 MHz, was used for the characterization of devices in the microwave frequency range. This procedure also can be applied under many other different conditions.

For example, Figure 2 illustrates the transmission characterization.

The input signals at ports [l.sub.A] and [L.sub.B], [R.sub.A] and [R.sub.B] can be written respectively, [V.sub.LA] = [A.sub.L] COS ([[Omega].sub.L] t + [[Phi].sub.AL]) [V.sub.LB] = [A.sub.L] COS ([[Omega].sub.L] t + [[Phi].sub.BL]) [V.sub.RA] = [A.sub.R] COS ([[Omega].sub.R] t + [[Phi].sub.AR]) [V.sub.RB] = [A'.sub.R] COS ([[Omega].sub.R] t + [[Phi].sub.BR]) and consequently the signals [V.sub.A] and [V.sub.B] are, [V.sub.A] = [K.sub.A] [A.sub.L] [A.sub.R]/2

* COS [([Omega.sub.L] - [Omega.sub.R]) t + [Phi.sub.AL] - [Phi.sub.AR] [V.sub.B] = [K.sub.B] [A.sub.L] [A'.sub.R]/2

* COS [([Omega.sub.L] - [Omega.sub.R] t + [Phi.sub.BL - [Phi.sub.BR] where, [K.sub.A] [K.sub.B] = conversion efficiencies
```                      of the mixers.
[Phi.sub.AL]         = [Phi] * L + K [Omega.sub.L] [I.sub.LA]
[Phi.sub.BL]         = [Phi] * L + K [Omega.sub.L] [I.sub.LB]
[Phi.sub.AR]         = [Phi] * R + K [Omega.sub.R] [I.sub.RA]
[Phi.sub.BR]         = [Phi] * R + K [Omega.sub.R] [I.sub.RB] + [Phi.sub.x]
```

[A.sub.L], [A.sub.R] = amplitude of the signal
```                       at the power splitter
outputs
```

[Omega.sub.L], [Omega.sub.R] = angular frequencies
```                               of the signal generators
GL and GR
[A'.sub.R]                    = [A.sub.R] * [A.sub.X]
```

with
```[Phi] * L, [Phi] * R   = phase noise of the
signal generators
```

k [Omega] L,
```k [Omega] R            = phase constant along
with pathways [I.sub.LA], [I.sub.LB],
[I.sub.RA], [I.sub.RB]
```

[Phi.sub.x], [A.sub.x] = phase and amplitude
```                         response of the device
under test at the
frequency [Omega.sub.R]
```

By substituting Equation 3 into Equation 2 results, [V.sub.A] = [K.sub.A] [A.sub.L] [A.sub.R]/2

* COS [([Omega.sub.L] - [Omega.sub.R])t + ([Phi] * L - [Phi] * R])

+ K ([Omega.sub.L] [I.sub.LA] - [Omega.sub.R] [I.sub.RA])] [V.sub.B] = [K.sub.B] [A.sub.L] [A.sub.R] [A.sub.x]/2

* COS [([Omega.sub.L] - [Omega.sub.R]t + ([Phi] * L - [Phi] * R])

+ K ([Omega.sub.L] [I.sub.LB] - [Omega.sub.R] [I.sub.RB]) - [Phi.sub.x]]

(4)

Finally for the outputs [V.sub.u1], [V.sub.u2] from the network analyzer we obtain, (5) [Mathematical Expression Omitted] If,

[K.sub.A] = [K.sub.B] and [I.sub.LA] = [I.sub.LB]

[I.sub.RA] = [I.sub.RB]

(6)

Equation 5 yields,

[V.sub.u1] = [A.sub.x]

[V.sub.u2] = -[Phi.sub.x]

(7)

Equation 7 shows that by comparing [V.sub.A] and [V.sub.B] in a low frequency vector analyzer, the phase and amplitude response of the device being tested can be measured at frequency [Omega.sub.R].

The fundamental condition in Equation 6 easily can be fulfilled by using, for example, two line stretchers at the inputs [L.sub.A] and [L.sub.B] of the mixers.

Wideband characterization of the device being tested can be obtained by varying [Omega.sub.R] and simultaneously, [Omega.sub.L], provided that their difference fall within the VNA bandwidth and [Omega.sub.L] and [Omega.sub.R] fall within the operating frequency range of the microwave components used. [Figures 1 and 2 Omitted]

Mauro Bramanti received his degree in electronic engineering from the University of Pisa, Italy in 1964, and his Libera Docenza degree from Italian Instruction Ministry in 1971. In 1965, he joined the Italian Consiglio Nazionale delle Ricerche (CNR), where his scientific activity is devoted to very high frequency techniques for telecommunication and industrial controls and measurements. Since 1978, he has been the coordinator of the Signal and Image Processing Department of the CNR Instituto di Elaborazione delle Informazione. His main interest lies in signal acquisition and processing methods and algorithms for noninvasive/nondestructive techniques.
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Title Annotation: Printer friendly Cite/link Email Feedback Application Note Bramanti, Mauro Microwave Journal Mar 1, 1990 822 Higher modes in insulating beads. Understanding system simulation with modulated carriers. Electronic circuits Network analyzers

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