Experimental Study of an Adding Interferometer at Millimeter Waves

Abstract

In order to study an original detection architecture for future cosmology experiments based on wide band adding interferometry, we have tested a single baseline bench instrument based on commercial components. The instrument has been characterized in the laboratory with a wide band power detection setup. A method which allows us to reconstruct the complete transfer function of the interferometer has been developed and validated with measurements. This scheme is useful to propagate the spurious effects of each component till the output of the detector.

Appendix

We consider here a two ports device. The source generator is connected to port 1 and a matched load to port 2. We then have an incident wave $V_{1}^{+}$ to the DUT (Device Under Test). The wave reflected from the device back to port 1 is $V_{1}^{-}$. The signal traveling through the DUT and toward port 2 is $V_{2}^{-}$. Any reflection from the load is $V_{2}^{+}$.

We can express the transient E field in term of voltages as in [3]:

$$ E_{1}=\frac{\left(V_{1}^{+}e^{-i\beta_{1}}+V_{1}^{-}e^{i\beta_{1}}\right)}{c}\,\,e(x,y) $$

(13)

$$ E_{2}=\frac{\left(V_{2}^{+}e^{-i\beta_{2}}+V_{2}^{-}e^{i\beta_{2}}\right)}{c}\,\,e(x,y) $$

(14)

where e(x,y) is the variation of the amplitude of the field propagating inside a waveguide section and c is a geometrical parameter. These variables are set to constants because of the common waveguide shape along the chain (cascade of components). E ₁ and E ₂ are the fields in the input and in the output of the device and β ₁ and β ₂ are their respective phases. In order to express E2 with E1, we need to consider the same base (the same propagation direction of the wave). Let’s set the propagation from port 1 to 2 as positive and from 2 to 1 as negative. This gives

$$ E_{2}=\frac{\left(V_{2}^{+}e^{i\beta_{2}'}+V_{2}^{-}e^{-i\beta_{2}'}\right)}{c}\,\,e(x,y) $$

(15)

with β ₂′ = − β ₂.

Finally, expressing E ₂ in terms of E ₁ and using the S parameters definition as in [3], we obtain:

$$ E_{2}=\left(\frac{S_{21}e^{-i\beta_{2}}+\left(\frac{S_{11}}{S_{12}}\right)e^{i\beta_{2}}}{e^{-i\beta_{1}}+S_{11}e^{i\beta_{1}}}\right) E_{1}. $$

(16)