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 virginiadiodes.com).
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 # 6BP71650/1000-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.
Mixer
IF Amplifier
Power Meter
5.6789 Watts
RF Input
1.0 GHz IF
bandpass filter
Local
Oscillator
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.
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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.
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 W 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.
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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.
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
Tamplifer
40K
Lmix
12dB
where Tamplifier is calculated from the amplifier noise temperature
Tmix  Tmeasured 

 Tmeasured 
NF  ln 10
Tamplifier  290exp
K  290K  40K
 10

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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106 Kelvin
300 Kelvin
77 Kelvin
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 virginiadiodes.com, 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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Pc 

f2
f1
D2 A0 c

 u d
4R 2  4
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. f = f2 – f1 is always 1.0 GHz, due to the bandpass
filter.
Energy per unit volume per unit frequency
The energy density u() is calculated using the photon energy h, the density of states,
and the Einstein-Bose probability function.
8h
u   3 
c
3
 h

exp
1
kb T 
Equation 2
Factor of c/4

The factor c/4 is to change from energy passing through a volume with length x 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 2,
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 W Collected power = 0.37 W
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.
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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 W 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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