THz absolute power measurements by heterodyne mixer



THz absolute power measurements by heterodyne mixer

We describe the THz power measurement of a photomixed source in the Optical Sciences lab at the University of Arizona for Prof. Jerome Maloney. A heterodyne receiver with bandwidth from 800 to 840 GHz was set up primarily to obtain spectra of the source described elsewhere with resolution to 10 kHz linewidth. At the same time, an estimate of the absolute THz power was made to compare to the more authoritative measurement made with a Golay Cell from MicroTech Instruments, also described elsewhere.

A few caveats first about THz power measurements. Firstly, THz beams confined by quasi-optical systems (Feedhorns and lenses) often are difficult to accurately analyze due to unknown beam propagation and indices of refraction for lenses, and diffraction effects due to the large wavelength in comparison to optical components such as the photomixer crystal. Additionally, a coherent measurement technique requires a flat phase front be coupled into the receiver, as well as the possibility of standing waves generated from any poor impedance matching of the THz beam.

Secondly, calibration of instruments must be made based on analytical solutions with various assumptions about material parameters and responses.

Equipment used in this measurement included

1) Schottky diode mixer receiver with LO from Virginia Diodes mixer model number WR1.2SHM (specs available online ).

2) IF Amplifier from Miteq model # AMF-3F-010020-04-13P at +15V. A Noise figure for this amplifier of 0.4 dB specified at 23 Celsius is 28 degree Kelvin noise temperature. At an operating temperature of 60 Celsius, the noise fgure has increased to 0.77, or 52 degree Kelvin.

3) Lorch Microwave 1.0 GHz IF Bandpass centered at 1.65 GHz, model # 6BP7-1650/1000-S.

4) Agilent Power Meter head and controller model #’s E9300A and E4418B.

5) Linux PC and software to sweep LO frequency and record power meter reading.

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We will not estimate THz power emitted from the photomixer source but not collected in the receiver. This is an unknown quantity until such time as the beam is mapped using our X-Y translation antenna range. A rough estimate may be found elsewhere.

Raw Data

Sweeping the local oscillator (LO) from 800 to 840 GHz in 1 GHz steps, with a 1 GHz bandpass IF filter integrates power within each 1 GHz band and displays the IF power on the power meter. In Figure 1, we can see that the peak of the THz output power is centered at 819.5 GHz. The dropout of data from 814 to 819 GHz is due to inefficiencies in the LO, leading to underpumping of the mixer. The data here is not recoverable because the heterodyne receiver is not sensitive in this range. A Gaussian fit has been shown in Figure 1 as well, and is used in the estimate of photomixed power output.

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Figure 1 – The Y-Factor (receiver sensitivity) is shown from 800 to 840 GHz in red. Notice the drop in sensitivity in the region from 812 to 819. The indicated IF power is shown in Solid Blue, with a Gaussian fit shown in Dotted Black over the insensitive region.

At 820 GHz, the peak of the collected data, the power meter indicated 57 mW of IF power. This information is used with a calibration of mixer response to determine RF power input in Watts.

Calibration data

A technique often used and accepted in THz radio astronomy is calibration of IF power output with two blackbody sources of known temperatures and expected RF power input from analysis. We’ve used a room temperature (taken to be 300 Kelvin) Eccosorb C-100 absorber and the same absorber placed in a Styrofoam cup full of boiling liquid Nitrogen (taken to be 77 Kelvin). The Styrofoam cup and LN2 is assumed to be largely transparent to THz radiation.

Background information. A figure of merit for heterodyne mixer receivers is their Noise Temperature Tmix, with the Noise Power NEP = kB * Tmix * BW. Boltzmann’s constant is kB, and the bandwidth of the measured IF (1 GHz due to the bandpass filter) is included in the factor BW. The common measurement is to look at the double sideband IF power output at two known temperatures, usually 77K and 300K, and determine a mixer noise temperature from Tmix = (Thot – Y * Tcold ) / (Y-1) where Y is the “Y-Factor” determined from the ratio of IF powers at Thot = 300K and Tcold = 77K. The measured Tmix on this day was 5000 Kelvin at 821 GHz, and 7100 Kelvin at 827 GHz.

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Figure 2 – Mixer noise temperature over 800 to 840 GHz receiver bandwidth after subtracting the IF amplifier contribution. Spec for this device is advertised at 5000K.

The noise temperature of the mixer alone is then calculated removing the contribution of the IF amplifier. The MITEQ amplifier has a 0.4 dB noise figure at 23 ºC, increasing 0.01 dB / ºC to 0.77dB an operating temperature of 40 ºC. The noise figure of the mixer is then

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where Tamplifier is calculated from the amplifier noise temperature

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At 820 GHz, the hot and cold measured IF power were 88.4 nW and 86.2 nW respectively. The listed noise floor of the power meter used was 100 pW, the noise power of the mixer and IF amplifier is 60 to 160 pW.

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Figure 3 – The calibration between collected RF power coupled into the mixer versus indicated IF power readout on the Agilent power meter.

Optical arrangement for calibration and measurement

We go in reverse of the light path for the calibration measurement. The aperture size of the detector is taken to be the area of the diagonal feedhorn which is 2mm x 2mm. The opening angle and beamwaist are specified for this horn at , feedhorn model # WR-1.2. Beam waist is 0.83 mm. Using Gaussian optics and expanding the beam to a distance of R = 2 cm, where the 300K and 77K blackbody surfaces were placed, the integrated area of the Gaussian spot at the 1/e2 points is A0 = 26 mm2.

These data are used to determine both the total blackbody power emitted by the calibration surface, and the percentage of this power intercepted by the detector.

Analysis

The first step of analysis was to calibrate the IF power to RF power. Because the IF output power of the mixer depends on RF input power, mixer loss (about 10 dB), the IF amplifier (about 20 dB), and LO power, (1-3 mW but variable across the receiver bandwidth) a direct calculation is sometimes not possible.

Instead, we calibrate at two known temperatures, calculating the received blackbody power. The IF power to RF power conversion is done by drawing a straight line (assuming this relation is linear) and finding the slope of the curve. This calibration can change by a factor of two across the receiver bandwidth, largely following the mixer noise temperature.

Equation 1 was used to calculate the power collected by the receiver.

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Equation 1

where f1 and f2 are the upper and lower edges of the RF input frequency determined by the LO tuning from 800 to 840 GHz. Df = f2 – f1 is always 1.0 GHz, due to the bandpass filter.

Energy per unit volume per unit frequency

The energy density u(n) is calculated using the photon energy hn, the density of states, and the Einstein-Bose probability function.

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Equation 2

Factor of c/4

The factor c/4 is to change from energy passing through a volume with length Dx per unit time to power by using the speed of light c, and a factor of ½ to include only out-flowing radiation. Another factor of ½ includes the angular dependence of the radiation into 2p, which is a Cosine relation.

Emittance per solid angle and solid angle subtended by receiver

The area A0 is the amount of blackbody radiation we are emitting from a Lambertian surface, while we lose radiation collected at an aperture of diameter D due to the inverse square law at 1/R2. [IR handbook, Volume 3 pg 116]

Using only one point in the receiver tuning, that of our numerical examples above 820 GHz, we perform the integral above over 1 GHz bandwidth and summarize the results in table 1.

THz IF power = 57.1 mW Collected power = 0.37 mW

300K IF power = 88.4 nW Collected power = 15.1 pW

77K IF power = 86.2 nW Collected power = 3.17 pW

Notice that the ratios of measured IF power to collected power (a calculated quantity) are not equal for 300K and 77K, this is due to the finite noise temperature of the detector. If the mixer noise temperature Tmix = 0 ºK, these ratios would be equal.

By summing over the range from 800 to 840 GHz in 1 GHz steps, and using the mixer calibration determined at each 1 GHz frequency interval, 3.0 mW is coupled into the mixer, assuming the Gaussian fit, and some average sensitivity in the region from 812 to 819 GHz.

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77 Kelvin

300 Kelvin

106 Kelvin

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