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A Novel Precision Real-Time Material Inspection System Using Cascaded Wide Gain Range Amplifiers With High Modulation Bandwidth Christian Hoffmann, Tobias Hermann, Peter Russer Lehrstuhl für Hochfrequenztechnik, Technische Universität München Arcisstr. 21, 80333 München Email: [email protected] Abstract—In this paper, the authors present the design and implementation of a microwave oscillator circuit with ultra- fast amplitude control for an inspection system appropriate for real-time measurements of continously streaming materials. The material passing through the resonator of the oscillator changes the resonance frequency and the quality factor of the resonator. This influences the oscillation frequency and the loop gain required for maintenance of stationary oscillation in the linear regime. From the measurement of the oscillator frequency and the gain, adjusted via an automatic gain control (AGC), resonance frequency and loaded quality factor of the resonator and therefrom the material parameters, i.e. material density and humidity, can be determined. For the automatic gain control circuit, a Gilbert-cell based variable gain amplifier (VGA) with high modulation bandwidth of 70 MHz and wide linear gain range is designed using SiGe HBTs. Cascaded variable gain amplifiers with a wide linear gain range of over 40 dB and an ultra-high control loop-bandwidth allow to measure the parameters of materials streaming at a velocity of around 10 m/s with an error in the order of 1 %. I. I NTRODUCTION Contact-free techniques to determine material parameters have gained growing importance over the last decades. There are several approaches achieving this goal by exploiting the interaction of matter and electromagnetic fields, for example using open-end coaxial resonator probes to determine the degree of moisture in brickwork. An important field of application is real-time quality control in industrial processes. In [1], a material inspection system employing a microwave cavity resonator is described. The two-port resonator is the frequency-determining part of a microwave oscillator. Solid materials or non-aqueous liquids streaming through the resonator cause a change of the reso- nance frequency and the quality factor of the resonator. This influences the oscillation frequency and the required amplifier gain for maintaining a given oscillator amplitude in the linear regime of the oscillator amplifier. By measuring the oscillation frequency f osc and the attenuation G, material parameters like the relative dielectric constant ε r can be calculated. A two-port oscillator usually is formed by a nonlinear active two-port and a frequency-dependent linear feedback two-port. The output signal of the frequency-dependent two- port is amplified in the active two-port and then fed back to the input of the frequency-dependent two-port. A necessary condition for stationary harmonic oscillation is, that the phase and the amplitude of the signal, after passing both two-ports, are unchanged [2] [3]. For the amplifier transfer function A(ω) and the resonator transfer function B(ω), the amplitude and phase conditions for sustained oscillations are [5]: |A(ω)|·|B(ω)| = 1 (1) A(ω)+ B(ω) = k · 2π, k N. (2) In harmonic oscillators, frequency and amplitude are deter- mined by the amplitude and phase conditions, since due to the frequency dependence of the linear feedback network, the phase condition is fulfilled for a certain frequency only, and due to the nonlinearity of the amplifier, the amplitude condition is fulfilled for a certain amplitude only. Different from the usual principle of operation of harmonic oscillators, in this work, we are using an amplifier in its linear regime and maintain a constant amplitude of oscillation by a fast automatic gain control of the amplifier. The amplifier gain, set by the automatic gain control, is a measure for the quality factor of the two-port resonator used as the frequency-dependent linear feedback two-port. Part of the oscillator signal is coupled out for frequency and amplitude measurement. The frequency is measured by a frequency counter. The momentaneous amplitude of the oscillator signal is sensed by a fast peak detector. A gain control circuit is used to keep the oscillator amplitude constant. The control voltage is a measure for the momentaneous quality factor of the resonator. A sufficiently low time constant of the control circuit allows an accurate measurement of a rapidly varying loaded quality factor of the resonator. The empty resonator has a loaded quality factor Q Lo of about 3200 in order to provide a high measurement resolution. The inserted material with quality factor Q m yields a reduction of the loaded quality factor to Q Lm . The loaded quality factor of the resonator with inserted material Q Lm is determined by 1 Q Lm = 1 Q Lo + 1 Q m . (3) This implies the need for a very high control bandwidth in the order of 10 - 50 MHz for the AGC because of the corresponding short settling time of the system.

[IEEE 2009 German Microwave Conference (GeMIC 2009) - Munich, Germany (2009.03.16-2009.03.18)] 2009 German Microwave Conference - A Novel Precision Real-Time Material Inspection System

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A Novel Precision Real-Time Material InspectionSystem Using Cascaded Wide Gain Range

Amplifiers With High Modulation BandwidthChristian Hoffmann, Tobias Hermann, Peter Russer

Lehrstuhl für Hochfrequenztechnik, Technische Universität MünchenArcisstr. 21, 80333 MünchenEmail: [email protected]

Abstract—In this paper, the authors present the design andimplementation of a microwave oscillator circuit with ultra-fast amplitude control for an inspection system appropriatefor real-time measurements of continously streaming materials.The material passing through the resonator of the oscillatorchanges the resonance frequency and the quality factor of theresonator. This influences the oscillation frequency and the loopgain required for maintenance of stationary oscillation in thelinear regime. From the measurement of the oscillator frequencyand the gain, adjusted via an automatic gain control (AGC),resonance frequency and loaded quality factor of the resonatorand therefrom the material parameters, i.e. material density andhumidity, can be determined. For the automatic gain controlcircuit, a Gilbert-cell based variable gain amplifier (VGA) withhigh modulation bandwidth of 70 MHz and wide linear gainrange is designed using SiGe HBTs. Cascaded variable gainamplifiers with a wide linear gain range of over 40 dB andan ultra-high control loop-bandwidth allow to measure theparameters of materials streaming at a velocity of around 10 m/swith an error in the order of 1 %.

I. INTRODUCTION

Contact-free techniques to determine material parametershave gained growing importance over the last decades. Thereare several approaches achieving this goal by exploiting theinteraction of matter and electromagnetic fields, for exampleusing open-end coaxial resonator probes to determine thedegree of moisture in brickwork.

An important field of application is real-time quality controlin industrial processes. In [1], a material inspection systememploying a microwave cavity resonator is described. Thetwo-port resonator is the frequency-determining part of amicrowave oscillator. Solid materials or non-aqueous liquidsstreaming through the resonator cause a change of the reso-nance frequency and the quality factor of the resonator. Thisinfluences the oscillation frequency and the required amplifiergain for maintaining a given oscillator amplitude in the linearregime of the oscillator amplifier. By measuring the oscillationfrequency fosc and the attenuation G, material parameters likethe relative dielectric constant εr can be calculated.

A two-port oscillator usually is formed by a nonlinearactive two-port and a frequency-dependent linear feedbacktwo-port. The output signal of the frequency-dependent two-port is amplified in the active two-port and then fed back tothe input of the frequency-dependent two-port. A necessary

condition for stationary harmonic oscillation is, that the phaseand the amplitude of the signal, after passing both two-ports,are unchanged [2] [3]. For the amplifier transfer function A(ω)and the resonator transfer function B(ω), the amplitude andphase conditions for sustained oscillations are [5]:

|A(ω)| · |B(ω)| = 1 (1)

∠A(ω) + ∠B(ω) = k · 2π, k ∈ N. (2)

In harmonic oscillators, frequency and amplitude are deter-mined by the amplitude and phase conditions, since due tothe frequency dependence of the linear feedback network,the phase condition is fulfilled for a certain frequency only,and due to the nonlinearity of the amplifier, the amplitudecondition is fulfilled for a certain amplitude only. Differentfrom the usual principle of operation of harmonic oscillators,in this work, we are using an amplifier in its linear regime andmaintain a constant amplitude of oscillation by a fast automaticgain control of the amplifier. The amplifier gain, set by theautomatic gain control, is a measure for the quality factor ofthe two-port resonator used as the frequency-dependent linearfeedback two-port.

Part of the oscillator signal is coupled out for frequencyand amplitude measurement. The frequency is measured bya frequency counter. The momentaneous amplitude of theoscillator signal is sensed by a fast peak detector. A gaincontrol circuit is used to keep the oscillator amplitude constant.The control voltage is a measure for the momentaneous qualityfactor of the resonator. A sufficiently low time constant of thecontrol circuit allows an accurate measurement of a rapidlyvarying loaded quality factor of the resonator.

The empty resonator has a loaded quality factor QLo ofabout 3200 in order to provide a high measurement resolution.The inserted material with quality factor Qm yields a reductionof the loaded quality factor to QLm. The loaded quality factorof the resonator with inserted material QLm is determined by

1QLm

=1

QLo+

1Qm

. (3)

This implies the need for a very high control bandwidthin the order of 10 - 50 MHz for the AGC because of thecorresponding short settling time of the system.

u uOut1 Out2

I

I

0

0

2I0

2

VCC

-VCC

uIN -uIN

R R

R R

C C

IN IN

Q1 Q2

Fig. 1. Transistor modulator with npn-bipolar transistors

In [1], an IQ Modulator is the actuator to set the gain andphase in the oscillator circuit. The control signal obtained froma field programmable gate array (FPGA) in amplitude/phaserepresentation is converted into inphase/quadrature representa-tion. Although, in principle this could be considered to be anelegant and versatile solution, the required circuitry includinga pair of analog four-quadrant multipliers and digital-to-analog converters (DAC) increases complexity and cost andpotentially decreases AGC loop stability.

Several approaches for an alternative method to control theRF oscillator signal amplitude have been analysed. Voltage-variable attenuators using cascaded GaAs MesFET drain-source paths provide the required speed and attenutation range,but exhibit a high change in RF phase-shift over the range ofattenuation. This violates the phase condition given in (2).

II. GILBERT-CELL VARIABLE GAIN AMPLIFIER

Mixer circuits can be used as control elements in variablegain amplifiers (VGA) and modulators. As a conversion gainhigher than unity is the design goal, an active multiplier circuitrealized with a bipolar transistor Gilbert-cell was favored overa passive approach using diodes.

A. Mode of Operation

Fig. 1 shows the basic layout for a mixer/ modulator circuitusing a pair of npn-bipolar transistors. This architecture isderived from the Gilbert-cell [4]. With this topology, thetransconductance gm = ∂iC

∂uBEof the transistors and therefore

the differential amplifier gain can be changed by injecting thecollector currents iC via a current source.

Taking a simplified small-signal transistor-model into ac-count [6], the single-ended output voltage uout can be written

VC

IC

VOut1

VOut2

VOut

VIN

EmitterFollowers

CurrentSource

ChipBalun

DifferentialAmplifier

Fig. 2. Block diagram of the VGA

TABLE IMEASUREMENT RESULTS

Parameter @2,5 GHz typ.linear gain range 21,4 dBrel. phase change 25,9◦Control bandwidth 70 MHzP1dB (PIN) −7,5 dBm

as

uOut = uOut1 − uOut2 (4)

=gm

2· rBERC

(rBE + RIN)uIN +

(VCC − RCI0

2

)(5)

−(−gm

2· rBERC

(rBE + RIN)uIN +

(VCC − RCI0

2

))

= gm · rBERC

rBE + RIN· uIN. (6)

with the small-signal base-emitter input impedance rBE of thetransistor, the load resistance RC , the injected current I0 andthe input voltage uIN.

B. Implementation

The block diagram of the variable-gain amplifier is shown inFig. 2. To achieve the required gain at 2.5 GHz in combinationwith low 1/f-noise, a SiGe Hetero-Bipolar-Transistor (HBT)was chosen. With this transistor, an amplifier stage with 16 dBgain and a noise figure of 0.6 dB at 2.4 GHz was realized.These values have been measured at a collector bias currentof 6 mA. In order to achieve high modulation bandwidth, thesame HBT type was used as the controlled current source.Chip inductors were selected as load impedances to achieveresonance with the capacitive collector impedances and there-fore increase maximum gain. Emitter follower circuits pro-vide the differential output signal. Input and output of theVGA both exhibit single-ended configuration. This ensureseasy integration with the other elements in the RF oscillatorloop, which also exhibit single-ended connectors. The circuitwas manufactured in hybrid technique on a glass reinforcedhydrocarbon/ceramic RF substrate.

2.4 2.42 2.44 2.46 2.48 2.5 2.52 2.54 2.56 2.58 2.6−80

−70

−60

−50

−40

−30

−20

−10P

ower

/ dB

m

Frequency / GHz

Fig. 3. Output spectrum at fMod = 70 MHz

C. Measurement Results

The measurements on the VGA were conducted using aHP 8753C vector network analyzer and some results are givenin Table I. With this topology, a linear gain range �G of over21 dB can be achieved. The relative phase-shift over this rangeis around 25 degrees, which ensures, that the phase condition(2) is adequately met in the RF oscillator circuit.

The modulation bandwidth was measured by applying amodulation signal with the frequency fMod to the input ofthe current source and viewing the amplitude modulation on aspectrum analyzer as seen in Fig. 3. The modulation propertieshave been investigated for fMod up to 70 GHz. Although thecircuit is in principle suitable for even higher modulationfrequencies, asymmetries in the prototype assembly lead tophase differences, that produce unequal sideband amplitudesat higher modulation frequencies.

III. THE MEASUREMENT FRONTEND

The variable-gain amplifier described in the previouschapter was used in the measurement system’s amplitude-controlled oscillator. Fig. 4 shows the block diagram of thewhole measurement system. Inside the box, the RF frontend,i.e. the whole RF circuitry except the resonator, is drawn.

A. The Oscillator Circuit

The oscillator circuit consists of the microwave cavityresonator, two cascaded VGAs and amplifiers with fixed gain.InGaP amplifiers have been chosen in order to achieve alarge, controllable linear gain range of the system of morethan 40 dB. The required additional electrical length of thefeedback circuit to fulfill the phase condition (2) is providedby a inserted coaxial waveguide segment.

To implement the automatic gain control, part of the os-cillator signal sO is coupled out of the loop by a low-temperature co-fired ceramic directional coupler component.This signal s1 is fed to a Wilkinson-type divider. One of itsoutput ports provides a signal s2 to a frequency counter for

FrequencyCounter ADC

Detector

VGADirectionalCoupler Cavity

Resonator

sC

sO

s1

s2 s3sd

ControlUnit

Fig. 4. Block Diagram of the Measurement Frontend

Fig. 5. Measurement Frontend

the measurement of the current RF loop oscillation frequency.The other port feeds an equal signal s3 to a fast level detectorIC operating as a peak detector. The detected signal sd is fedinto the control unit.

B. The Controller

The control-unit is based upon a high-speed operational am-plifier in a PI-controller topology to enable very high controlbandwidths in excess of 50 MHz. Due to its FET inputs, it isvery well suited for use as an integrator, because low leakagecurrents ensure high precision. A precision voltage source isused as a setpoint reference.

An integral term is added in order to minimize the residualcontrol error and to ensure an accurate measurement of the RFloop gain. The transfer function GPI(s) of the PI-controller isgiven by

GPI(s) = KPr

(1 +

KI

sKPr

), (7)

with the proportional gain KPr and the integral gain KI [7].The signal sC is a direct measure of the current oscillator

loop gain. sC is therefore analog-to-digital converted. In orderto eliminate high-frequency noise and to limit the bandwidthof sC to half the sampling rate, the signal sC is filtered byan active lowpass-filter. The sampled signal is processed by

−4.2 −4.1 −4 −3.9 −3.8 −3.7 −3.6 −3.5 −3.4 −3.3−20

−10

0

10

20

30

40

−4.2 −4.1 −4 −3.9 −3.8 −3.7 −3.6 −3.5 −3.4 −3.3−100

−90

−80

−70

−60

−50

−40

angl

e S

21 /

deg

Transmission FactorTransmission Phase

--

Control Voltage C

/ V

|S21

| / d

B

Fig. 6. S21 at f = 2.535 GHz, unloaded resonator

2.52 2.525 2.53 2.535 2.54

−90

−85

−80

−75

−70

−65

−60

−55

−50

−45

−40

−35

Frequency / GHz

Pow

er /

dBm

loaded resonatorunloaded resonator

Fig. 7. RF signal spectra at different load conditions

the system’s signal processing unit, implemented on an FPGA[1].

The control signal sC is applied to the control inputs of thetwo cascaded VGAs in order to hold the oscillater amplitudeconstant on its prescribed value. By this way the amplitudecondition (1) is fulfilled in the linear amplifier regime.

The RF frontend circuit was fabricated on a glass reinforcedhydrocarbon/ceramic RF substrate in hybrid assembly. Fig. 5shows a photograph of the RF frontend.

IV. MEASUREMENT RESULTS

S-parameter measurements were conducted on the RF fron-tend. For this purpose, the RF oscillator loop with the cavityresonator was cut and connected to a vector network analyzer.A digitally controllable precision power supply provided thecontrol voltage signal sC to allow measurement of S21 versussC . The measured magnitude and phase of S21 of the cutoscillator loop with an empty resonator are presented in Fig. 6.

In the control voltage range from −4.25 V to −3.6 V, thefrontend provides a wide linear gain range of over 40 dB. Thegain reaches 0 dB at around −4.25 V, in order to meet the

amplitude condition (1) for the case of an empty resonator.In the presence of lossy materials in the resonator, increasingsC to −3.6 V enables the measurement system to fulfill theamplitude condition for a 35 dB range of attenuation variation.As two cascaded VGAs are used, this gain range can beincreased beyond 40 dB using InGaP amplifiers with higherstatic gain.

According to Fig. 6, the relative change in phase-shift ∠S21

versus the control voltage sC is just over 50 degrees in thelinear gain range. This ensures, that the phase condition (2) isadequately satisfied.

The complete measurement system was tested under varyingresonator load conditions. Fig. 7 shows the change in reso-nance frequency induced by a moderate load composed ofdry material. A transmission measurement with the resonatoryields an attenuation of the resonator response with thismaterial by about 14 dB. The resonance frequency changesfrom 2.535 GHz to 2.522 GHz. The residual control error isless than 0.1 dB. This accounts for very accurate control of thegain in the oscillator loop and therefore a high measurementaccuracy via continous tracking of the control voltage sC canbe achieved.

V. CONCLUSION

The design and realization of a real-time material in-spection system for continously streaming materials utilizinga microwave oscillator has been presented. The oscillatoramplitude is held constant in the linear regime by an AGCemploying variable gain amplifiers with high modulation band-widths of 70 MHz. Their wide controllable linear gain rangeof over 40 dB enables the maintenance of stationary oscillationunder high resonator load conditions. The ultra-fast controllerloop achieves an extremely low control error of the oscillatoramplitude under 0.1 dB, enabling precision measurements ofmaterial parameters with an error in the order of 1 %.

In addition, the circuit complexity has been considerablyreduced in comparison to the previous approach [1], whilecontrol loop stability has been enhanced.

ACKNOWLEDGMENT

The authors would like to thank the BayerischeForschungssstiftung for supporting this project.

REFERENCES

[1] T. Hermann, G. Olbrich and P. Russer, A Novel Microwave-based In-spection System for Continuously Streaming Materials Using A CavityResonator, In European Microwave Conference, 2008, pages acceptedfor publication.

[2] K. März, Phasen- und Amplitudenschwankungen in Oszillatoren. Archivfür Elektronik und Übertragungstechnik, vol.24, no.11, pp.477-490, 1970.

[3] W. Mathis and P. Russer, Oscillator Design, in Encyclopedia of RFand Microwave Engineering, Ed.: Kai Chang , John Wiley and Sons,Hoboken, New Jersey, 2005.

[4] B. Gilbert, A precise four-quadrant multiplier with subnanosecond re-sponse. IEEE Journal of Solid-State Circuits, Volume 3, Issue 4, Dec1968 Page(s):365 - 373.

[5] F. Giannini and G. Leuzzi, Nonlinear Microwave Circuit Design. JohnWiley and Sons, Chichester, England, 2004.

[6] U. L. Rohde and D. P. Newkirk, RF / Microwave Circuit Design forWireless Applications. John Wiley and Sons, 2000.

[7] G. Schmidt, Grundlagen der Regelungstechnik. Springer, Berlin, 1994.