Development of an integrated am shortwave upconversion receiver front-end

DEVELOPMENT OF AN INTEGRATED

AM SHORTWAVE UPCONVERSION

RECEIVER FRONT-END

V

J.W.Th. Eikenbroek

TR diss

-q Cl JUs* O * *

DEVELOPMENT OF AN INTEGRATED

AM SHORTWAVE UPCONVERSION

RECEIVER FRONT-END

DEVELOPMENT OF AN INTEGRATED

AM SHORTWAVE UPCONVERSION

RECEIVER FRONT-END

Proefschrift

ter verkrijging van de graad van

doctor aan de Technische Universiteit Delft

op gezag van de Rector Magnificus, prof.drs. P.A. Schenck,

in het openbaar te verdedigen ten overstaan van een commissie

aangewezen door het College van Dekanen

op dinsdag 7 maart 1989, te 14.00 uur

door

Johannes Wilhelmus Theodorus Eikenbroek,

geboren te Delft,

elektrotechnisch ingenieur

Dit proefschrift is goedgekeurd

door de promotor

Dedicated to my wife Karin

CONTENTS

NOTATIONS

1 ARCHITECTURE OF A SHORT-WAVE UPCONVERSION RECEIVER FRONT-END 1

Introduction 1

1.1 Objectives 1 1.2 Architecture of a downconversion receiver 2

1.3 Architecture of an upconversion receiver 3 1.3.1 Receiver with an ideal IF filter 3 1.3.2 Receiver with a non-ideal IF filter 5 1.4 The single conversion receiver with a selective detector 6

1.4.1 General considerations 6 1.4.2 Example - 7 1.5 The front-end of the receiver 9

1.5.1 Noise optimization 9 1.5.2 Other considerations about the front-end 16

1.6 General considerations about the distortion 18

1.7 Discussion 21 References 23

2 NOISE OPTIMIZATION OF VARIOUS ANTENNA-AMPLIFIER COMBINATIONS 25

Introduction 25 2.1 The antennas 25

2.1.1 The whip antenna 26 2.1.2 The loop antenna 27 2.2 Definition of two reference antennas 29

2.3 Noise adaptation of the antenna to the amplifier 30

2.3.1 The reference transistors 31 2.3.2 Whip antenna and bipolar transistor 31

2.3.3 Whip antenna and a JFET 33 2.3.4 Whip-BJT versus whip-JFET 35 2.3.5 Loop antenna and a JFET 35 2.3.6 Loop antenna and a BJT 37 2.3.7 Deterioration of the SNR due to a finite rb 40

2.3.8 Discussion 41

2.4 S N Rw hjP versus SNRio o p 42

2.5 External noise 43 2.6 Discussion 45 References 46

3 DISTORTION ANALYSIS OF AGC STAGES AND MIXERS 47

Introduction 47 3.1 Development of the necessary mathematical tools 47

3.1.1 Operator definitions 48 3.1.2 Application to non-linear equations 49

3.1.3 Determination of the desired non-linear transfer

of a circuit 50 3.2 The transistor model 51 3.3 Current transfer of a differential pair 53

3.4 Distortion analysis of a single AGC stage 56 3.4.1 Distortion due to the finite source impedance 56

3.4.2 Distortion due to the base resistances 61

3.4.3 Discussion 68 3.5 Distortion analysis of a switching mixer 70

3.5.1 Distortion performance during the states at rest 70 3.5.2 Distortion during the transitions of state 72 3.5.3 Comparison of the various mixer distortion

mechanisms 81 3.6 Distortion of balanced configurations 82

3.6.1 The balanced AGC stage 83 3.6.2 The doublé balanced mixer 85 3.7 Influence of the impedance between external base nodes on

the distortion performance of balanced configurations 86

3.8 Discussion 90 References 92

4 SURFACE-ACOUSTIC-WAVE RESONATOR FILTERS 93

Introduction 93 4.1 Buik-wave resonators versus SAW resonators 94

4.2 Construction of a SAW resonator 94

4.3 The reflection grating 96 4.3.1 The reflection factor of a reflection grating 97

4.3.2 Reflection- and transmission factor of a

single strip 99 4.3.3 Reflection factor of the reflector near

synchronism 101 4.3.4 Zeros of the reflection factor 103

4.3.5 Characterization of a reflector 104

4.4 The interdigital transducers 105 4.4.1 The properties of an IDT 105 4.4.2 Transducer admittance 108 4.4.3 Circuit representation of a delay line 110

4.5 The resonator transfer 111 4.5.1 One-port resonator 111 4.5.2 Two-port resonator 117 4.5.3 Resonator transfer versus delay-line transfer 121

4.6 Placement of the IDTs within the cavity 122 4.7 Velocities within the resonator structure 125

4.8 Losses 126 4.9 Other modes and transverse modes 127

4.10 Frequency stability of the resonator 129

4.11 Coupled resonators 130 4.11.1 Transducer-coupled resonators 130

4.11.2 Resonator transfer versus delay-line transfer 132 4.11.3 Coupled resonators with a capacitive

source impedance 133 4.12 The source and load impedance of a resonator 136

4.13 Discussion 136 References 138

APPENDIX 1 THE NON-LINEAR TRANSFER OF A NEGATIVE-FEEDBACK

AMPLIFIER 139 Introduction 139 A.1 The asymptotic-gain model of a negative-feedback

amplifier 139 A.2 Summary of the mathematical tools 140

A.3 The non-linear asymptotic-gain model 141 A.4 Example of a non-linear transistor transfer 146

References 149

SUMMARY 150 SAMENVATTING 152 ACKNOWLEDGEMENTS 154 AB0UT THE AUTHOR 155

NOTATIONS

Throughout this thesis the fcllowing notations of quantities are used:

1) Capital letters and subscripts in capital letters represent constant (time independent) quantities.

For instance; a bias current lx, a supply voltage U B .

2) Small letters and subscripts in small letters represent time dependent quantities in the time domain such as signal quantities.

For instance; a signal base-current ib,

a signal voltage ug.

3) Small letters and subscripts in capital letters represent general time dependent quantities in the time domain. These quantities represent the sum of a constant part and a time dependent part.

For instance; a collector current ie = Ie + ie, a tail current ir = IT +

ig-4) Capital letters and subscripts in small letters represent signal quantities in the frequency domain. Generally these quantities are complex.

For instance; a signal base-current It,,

a signal voltage Ug.

5) The impulse response of a circuit. This is represented by a small letter and its corresponding frequency-domain quantity by a capital letter.

1 ARCHITECTURE OF A SHORT-WAVE UPCONVERSION RECEIVER FRONT-END

Introduction

This chapter presents a general description of the architecture of a short-wave upconversion receiver front-end. The front-end must be suited for integration as much as possihle. Conventional

downconversion receiver front-ends are not suited for integration because they use a tracking bandpass filter at the input of the receiver, tuned at the receiving frequency of interest. On the other hand, an upconversion receiver architecture is highly attractive for integration and is hence chosen for the front-end

[1.1].

First a short description of the architecture of a downconversion-and an upconversion receiver will be presented.

A very simple architecture of an upconversion receiver is possible if a channel-selective intermediate-frequency (IF) filter, with a sufficiënt stopband rejection, can be fabricated. However, for most upconversion receivers the IF frequency will be too high to realize such a filter. This makes it necessary to implement selectivity in the part of the receiver behind this non-ideal IF filter. One possibility is a selective synchronous detector and this is the solution we will be considering.

This thesis concentrates on the front-end of the receiver. In a subsequent thesis van der Plas [1.2] will describe the receiver part following the IF filter.

The front-end of the upconversion receiver cotnprises all the blocks of the receiver from the antenna input through to the first IF filter. In the subsequent sections we will briefly deal with the architecture of the entire, where upon we focus our attention on the architecture of the front-end. In addition some important parameters will be discussed which will serve as a figure of merit for the front-end.

1.1 Objectives

Our objective is the analysis and design of a front-end for a short-wave (SW) receiver for public broadcasting transmitters which is suited for integration. Single-sideband reception will not be considered.

The receiver must be designed for an optimum reception of the long-wave (LW), medium-wave (MW) and short-wave (SW) bands. These bands together cover the frequency range of 150 kHz through to 30 MHz.

The frequency allocation is approximately equal to LW : 150 kHz - 365 kHz,

MW : 512 kHz - 1625 kHz, SW : 1.8 MHZ - 30 MHz.

In addition the receiver must be designed for an optimum

performance and the power consumption should be kept at a minimum. This thesis presents a general description of the design of a front-end and given the specified frequency range, guidelines are indicated for choosing an optimum design.

Most of the analysis are directed towards the use of a bipolar integration process. As opposed to field effect transistors bipolar transistors have attractively large transfer parameters, such as the transconductance, at reasonable bias currents. In addition a high-frequency (NPN) bipolar process was readily available at the university [1.3]. In this process p-channel junction FETs (JFETs) are also incorporated tl.4] and these devices are at times included in the analysis.

1.2 Architecture of a downconversion receiver

In this section the architecture of a downconversion receiver will be described. Only a short description will be given here, but a more thorough treatment of different receiver architectures can be found in [1.1].

The architecture of a conventional downconversion receiver is depicted in figure 1.1. \|/ a n t e n n a tunable b a n d - p a s s I f i lter I ideal IF f ilter lacal osc i 1 lator ^> d e t e c t o r f i F < fr f

Figure 1.1 Architecture of a downconversion receiver (flf- < frt ) .

A mixer circuit performs a frequency conversion to a fixed intermediate (IF) frequency. This makes it possible to use a non-tunable bandpass filter at the IF frequency to select the desired channel from the converted spectrum. In a downconversion receiver the IF frequency is chosen lower than the lowest radio frequency (rf frequency) of interest. If the channel selective IF

filter is ideal then the desired audio information can be obtained by a non-selective detector such as an envelope detector.

However, frequency conversion makes the receiver sensitive to unwanted spurious frequencies. In a downconversion receiver these spurious frequencies can lie partly in the tuning range of the receiver and a tunable bandpass filter at the input of the receiver is necessary to suppress the unwanted channels. This bandpass filter must be tuned to the desired rf channel and to make this possible the input filter must be coupled to the local oscillator driving the mixer.

Due to the tunable bandpass filter at the input and its inherently required coupling to the local oscillator, the architecture of a downconversion receiver is not attractive for monolithical integration.

1.3 Architecture of an upconversion receiver

As will be shown the architecture of an upconversion receiver is much more attractive for monolithical integration.

Upconversion implies that the center frequency of the IF filter lies higher than the highest rf frequency of interest.

First the architecture of an upconversion receiver with an ideal channel selective IF filter will be discussed to illuminate this architecture. Next the architecture of a practical upconversion receiver will be examined.

The implementation of the receiver part following the IF filter will be described by van der Plas [1.2].

1.3.1 Receiver with an ideal IF filter

If we assume the channel selective IF filter to be ideal the architecture of an upconversion receiver is simple. Figure 1.2 shows this architecture.

\/ antenne image fiIter flF iüeal Ir f ilter detector out local osc i1lator

Although two frequency conversions take place in the receiver the receiver is usually called a single conversion receiver, neglecting the frequency conversion by the envelope detector.

An envelope detector is a non-selective detector but this is of no concern here because only the desired channel passes the IF filter. The simple architecture of the receiver consists of a non-tunable image and spurious filter at the input, plus a mixer, an IF band-pass filter and a detector.

The filter at the input must have a pass-band equal to the desired radio frequency (rf) band of interest. Thus no channel selection will take place! Due to the frequency conversion by the mixer the receiver becomes sensitive to other unwanted signals at its input. The purpose of the filter is to reject the signals at the image channel of the receiver and all other parts of the spectrum not belonging to the desired rf band. It is important to reject the input signals at the image channel of the receiver because these signals will also fall within the pass-band of the TF filter after conversion and have the same conversion gain as the desired

signals.

For the frequency converting device a balanced switching mixer will usually be used because it has the highest dynamic range and the best distortion performance [1.5]. The output signal of an ideal balanced switching mixer can be represented by the inultiplication of the input signal with a periodic square wave with peakvalues +1 and - 1 . The odd harmonies of this square wave signal couvert other parts of the input spectrum to the IF band and the input filter must also reject any spurious signals on these frequeneies of the spectrum. Spurious signals rejection is optimum if the local oscillator frequency is chosen to be much higher than the IF frequency.

As a rule of thumb the IF frequency should be chosen about three times higher than the highest rf input frequency of interest. If the IF frequency is chosen too close to the highest rf frequency a much higher order of the image and spurious rejection filter would be necessary to obtain optimum rejection of the various spurious signals [1.1] .

For the short-wave receiver the highest rf frequency is 30 MHz and an IF frequency of about 100 MHz is chosen.

As opposed to the conventional downconversion receiver architecture no preselection will take place until the I£ filter. This puts a burden on the noise and distortion performance of the circuits preceding the IF filter. For this reason the image and spurious filter must be a passive filter, which cannot be integrated even with state-of-the-art technology.

Note that no tunable filters are necessary in an upconversion receiver making it very attractive for monolithical integration. We will not go further into details about the architecture represented in figure 1.2 because a practical receiver will not

have an ideal channel selective IF filter and additional measures must be taken if the desired channel is to be selected under various receiving conditions.

1.3.2 Receiver with a non-ideal IF filter

Because in an upconversion receiver the IF frequency is higher than the highest rf frequency of interest it will usually not be

possible to realize adequate channel selection at this IF frequency in practice. Due to the non-ideal channel selection and the limited out-of-band rejection the part of the receiver behind this IF filter must contain extra selectivity to make an undisturbed reception of only the desired channel possible.

Two types of receiver architectures can be used to obtain this extra selectivity behind the (first) IF filter. Both are called doublé local oscillator receivers.

First a doublé conversion receiver can be used with a second conversion to a low second IF frequency where sufficiënt channel filtering can be accomplished by another band-pass filter, foliowed by for instance an envelope detector. Due to the low IF frequency of the second conversion an image band associated with this conversion will be close to the first IF band. The first IF filter must be able to suppress this image band suf ficiently.

The other method is to use a single conversion receiver with a selective detector. This method can be viewed as a doublé conversion receiver with a zero second IF frequency. The extra selectivity can now be obtained by way of a low-pass filter of sufficiënt order.

Figure 1.3 shows the architecture of a single conversion receiver with a selective detector.

\/ antenna

Figure 1.3 Architecture of a single conversion receiver with a selective detector.

The advantage of the last solution compared with the doublé

conversion receiver is the absence of another image frequency and a second IF band-pass filter, making it more suitable for

integration. Due to the above stated advantages of the single conversion receiver with a selective detector we will focus our attention to this receiver type.

We assume that the first IF filter has a reduced selectivity. Before the second conversion to zero frequency can take place the carrier must be regenerated with the appropriate phase. A phase lock loop (PLU provides a very applicable solution. The

regenerated carrier will be used to convert the spectrum behind the first IF filter to a spectrum around zero frequency. This second conversion to zero frequency will usually be done by a second switching mixer. After the conversion, the desired band can easily be filtered out by a low-pass filter of sufficiënt order.

1.4 The single conversion receiver with a selective detector

In the subsequent sections the single conversion receiver with a selective detector will be discussed in more detail.

1.4.1 General considerations

The front-end of the receiver must be able to handle the entire spectrum of the rf band without excessive distortion and noise production. Because the IF filter is not channel selective more than one channel will be present at the input of the selective detector and the PLL of the detector must be designed to lock and stay locked at the desired channel under all operating conditions. Problems arise when we want to lock on a desired channel having a very small signal level compared to that of an undesired adjacent channel. Behind the IF filter it is still possible that the signal level of the unwanted channel is much larger than that of the desired channel. If the loop bandwidth of the PLL is too large the unwanted channel can pull the VCO away from the desired channel and

the PLL will lock on the large signal of the undesired channel. To prevent this a very narrow loop bandwidth of the PLL must be

chosen, laying excessive demands on the frequency-set and stability of the local oscillator and VCO. In practice one has to resort to synthesizer tuning of the receiver.

Problems can also arise due to the signal-level dependent loopgain and loop bandwidth of the PLL. Measures must be taken to maintain a stable and well-behaved phase transfer and lock-in performance for all the different carrier levels at the input of the PLL. An AGC stage preceding the input of the detector can partially overcome this problem.

Even order distortion within the loop of the PLL generatés a DC offset and this offset cannot be distinguished from the actual DC signal level. Also the offsets present within the loop of the PLL will distort the information carried by the DC signal level. A novel offset compensated synchronous detector, making use of auto-zero techniques, is described by van der Plas [1.6].

In conclusion we can state that a single conversion receiver with a selective detector provides an elegant receiver concept suited for a maximum degree of integration. However, in practice the selective detector must be extended to overcome the various problems

associated with the imperfect IF filter.

1.4.2 Example

The example given here demonstrates the different signal-ranges that can occur in the various parts within the receiver. We assume that a single conversion receiver with a selective detector is used.

An important figure of merit of a receiver is its sensitivity. The sensitivity is defined as the required signal level at the input of the receiver to obtain a signal-to-noise ratio (SNR) of 26 dB at the output of the detector, measured in a 2.5 kHz noise bandwidth. The input signal must be a double-sideband AH signal, modulated by a 1 kHz tone with a modulation depth of 30%. The corresponding carrier-to-noise (CNR) ratio is 39.5 dB in a 5 kHz bandwidth. The ratio of the maximum signal which must be received with an acceptable level of distortion and the noise level in a certain bandwidth is called the dynamic range of the receiver. For a practical receiver this ratio amounts to about 130 dB with a noise bandwidth of 5 kHz. The corresponding dynamic range of the input signals is then 130 - 39.5 * 90 dB. This also implies that the AGC control range should approximately encompass 90 dB. Due to

distortion and noise considerations the AGC circuit should preferably be positioned in the part of the receiver where full channel selection has taken place. However the PLL can not handle the complete dynamic range properly. A compromise is to put a part of the AGC control range between the IF filter and the input of the selective detector. Van der Plas has shown that the PLL can handle a range of 50 dB [1.6] implying an AGC control range preceeding the detector of 40 dB. A single AGC stage can handle this range

(chapter 3 ) . The remaining AGC control range must be implemented within the selective detector.

Because no channel selection takes place in front of the IF filter the front-end must be_ designed to handle the full dynamic range. Suppose the IF band-pass filter consists of two coupled resonators

(chapter 4 ) . Due to the temperature dependence of the center

frequency of the filter and fabrication tolerances the bandwidth is chosen to be 18 kHz to ensure that under all conditions the desired channel remains within the passband of the filter. In Europe the

channel spacing is 9 kHz and the audio bandwidth is about 3.5 kHz. The resonators are critically coupled to obtain a flat passband. Due to a variety of reasons the stopband rejection is limited to 50 dB compared with the passband level. Figure 1.4 shows the filter curve around its center frequency.

Two coupled resonators, kQ = 1 Figure 1.4 Af (kHz) (log) One side of the pass-band transfer of two coupled

resonators, kQ = 1, Af = f - f0.

According to the specifications of the filter the adjacent channels will only be 3 dB suppressed by the IF filter if the receiver is

tuned to have the desired channel at the center frequency of the filter! The channels at a distance of two times the channel spacing will be 12 dB suppressed and channels at three times the channel spacing 19 dB. Even if a channel with maximum power is positioned far away from the desired channel, the suppression is at most 50 db and the detector must account for the remaining 40 dB.

Due to this imperfect IF filter the selective detector must be designed such that it can lock and stay in lock on the smallest signal while an adjacent channel can have the maximum allowed signal level. The difference in signal level can be up to 87 db! The IF filter has decreased the difference in signal level only by 3 dB. If the channel with maximum power is located at a distance of three times the channel spacing away of the desired channel the difference in signal level will at most be 71 dB.

These requirements of the synchronous detector are very difficult to realize without resorting to complicated and expensive

solutions. Alleviation is attained by using a more complex IF filter, but this also will be expensive. In practice a compromise must be found between the complexity of the IF filter and that of the selective detector within a prescribed environment.

1.5 The front-end of the receiver In this sect single conve in the previ front-end mu without gene channel sele circuits of architecture subsequent s more detail

ion we will focus our rsion receiver with a ous section. As expla st be able to handle rating too much noise ction will take place the front-end must be must be designed for ection all these cons

attention on the front-end of the selective detector as described ined in the previous section, the the full dynamic range properly

and distortion. Because no at the input all the active extremely linear and the

optimum noise performance. In the iderations will be discussed in

1.5.1 Noise optimization

Two essentially different situations for optimizing the signal to noise ratio of the front-end can be considered. While such

considerations have already been presented before [1.7], [1.8], the following treatment is believed to be simpler and more general. Figure 1.5 shows both situations.

V

ampli f ier image filter

IF filter

local /f\ \ (b) oscillator V _ >

Figure 1.5 Two possible upconversion receiver front-ends. (a) Image filter in front of amplifier.

(b) Amplifier in front of image filter.

The first situation is a front-end architecture with first the image and spurious rejection filter and then a buffer circuit

foliowed by the spurious and image rejection filter (figure 1.5-b). We will compare both situations for a reactive source-impedance; the source is a voltage source with a series capacitor in case of an electrically short whip antenna and the source is a shunt inductance if an electrically small loop antenna is considered

(chapter 2 ) . Both the open-terminal voltage of the whip and the short-circuit current of the loop antenna are frequency independent in relation to the incident EM-field.

To make a fair preamplifier in active device. real load imped noise performan thereby fixing addition we ass a bipolar trans

comparison possible we will assume that the

both cases only contributes noise due to its first In case of the filter foliowed by an amplifier a ance RL can be obtained without deteriorating the ce by using an amplifier with two feedback loops, the input impedance [1.9], [1.10], [1.11]. In

urne that the first active device of the amplifier is istor.

By way of an il loop antenna as

lustration the SNR for both combinations with the the source will be calculated and compared. a) Selective SNR optimization

First the situation with a filter foliowed by the amplifier will be discussed (selective SNR optimization). Figure 1.6 shows the

situations of interest. We assume the reactance of the antenna to be a part of the filter network.

reactive part of filter

(a) noise free _{ampli f ier}

"■O

\h

-e

Figure 1.6 Circuits for selective SNR optimization. (a) Loop antenna.

(b) Whip antenna.

The filters are assumed to be lossless.

Because both signal sources (Ia and Ua) have a frequency independent relation to the incident EM-field a frequency

independent transfer of the filter is also desired. Due to the type of reactance of the antennas only band-pass filters can be realized with a frequency independent signal transfer for the rf band of interest.

The noise sources un and in in figure 1.6 represent the equivalent

noise sources of the first active device of the amplifier. The

output impedance of the filter is denoted by Z0(s) with s the

Laplace variable.

[1.8] but here the SNR of the voltage across the input terminals of the amplifier will be considered. If we assume the filter transfer to be known the voltage across the input terminals of the amplifier can be determined as a function of frequency.

The circuit of interest can be represented by figure 1.7 if the SHR of the voltage across the input terminals of the amplifier is considered. Note that the resistance RL is noiseless.

noise free amp1i f ier

Figure 1.7 Equivalent circuit at the input of the amplifier.

According to figure 1.7 the spectral power density S(U„e) of the

equivalent noise voltage un e across the input terminals of the

amplifier is equal to(neglecting any correlation between un and in)

S(Un e) = RL2

IRL + Z0(s) I'

S(UD) + S(In IZ0(s) I _{' ) ■} (1.1)

with S(U„) and S(I„) representing the spectral power densities of un and i„ respectively.

Because lossless filters are considered, Z0(s) represents the

output impedance of a reactance network and will always be imaginary [1.12]. Due to the imaginary impedance we have

IRL + Zo s) I2 = RL + IZ0(s) I2. (1.2)

Substituting this into (1.1) results in

S(Une RL2

RL + IZo(s) I2

fs(u„

If the signal transfer of the filter is assumed to be frequency independent within the passband of the filter it is also desirable to have a frequency independent SNR within this band.

A noise spectrum independent of the value of IZ0(s)I can be obtained by choosing

S(U„) = S(I„) -RL . (1.4)

The remaining spectrum is then equal to

S(Une> = S ( I „ ) - R L . (1.5)

If equation (1.4) is not satisfied the noise spectrum will depend

on the value of IZ0(s) I and will vary between lower and higher

values than are given by (1.5).

With the aid of expressions (1.4) and (1.5) the equivalent spectral power density of the noise voltage across the input terminals of the amplifier can be determined.

Because we assume the first active device of the amplifier to be a bipolar transistor the spectral power densities of the noise

sources un and i„ are (see chapter 2)

S(U„) = 4kT[ rb + - i - ) ,

S(I„) =

4kT-2 1 2hF Ere

with rb the base spreading resistance, hp£ the DC common-emitter

current gain of the transistor and re the differential emitter

resistance as defined by

with k Boltzmanns constant 1.38-10 3 J/K, T the absolute

— j g

temperature and q the charge of an electron 1.6-10 C. Ie is the collector current of the transistor.

Substituting these equations in (1.4) and assuming rb much smaller

than re, the value of re necessary to satisfy (1.4) is

L e o p t (1.6)

fT~F

and the spectral density of the noise voltage is, according to (1.5)

S ( Un e)o p t = 4kT - ^ . (1.7)

S(Une)opt represents a white spectrum of the noise voltage across the input terminals of the amplifier.

If the impedance RL were realized by a resistor it can be shown that the noise spectrum would be higher than represented by (1.7) and depends on the value of Z0( s ) .

Within the pass-band of the filter the SNR is independent of frequency because both the signal transfer and the noise level at the input of the amplifier are frequency independent.

Hereafter the calculations will be performed with the loop antenna as the source.

The signal voltage at the input of the amplifier in this case is equal to Ï J ^ R L - Let SNRS denote the SNR in case of the selective SNR optimization, giving the expression

SNR

= -Lll£K^dïl , (1.8)

A k T "

where a noise bandwidth of 1 Hz is assumed.

As can be deduced from filter handbooks the value of RL is related

to the value of the source inductance La [1.13]. This relation is

almost independent of the order and type of filter transfer. For a bandpass filter the relation between RL and La is given by

RL

= _2ü:j!_iki_ . (i.

fr denotes the geometrie average frequency of the band-pass filter

and Af the bandwidth of the filter, hence fr2 = fL-fH ,

Af = £H - fL ,

where £L and fH are the -3 dB corner frequencies of the bandpass filter.

Substituting equation (1.9) into (1.8) finally results in

SNR

=

. (1.10)

/TkT^- /IT^

Equation (1.10) represents the SNR in the case of selective SNR optimization.

b) Wideband SNR optimization

Next the situation as depicted in figure 1.5-b will be discussed. The optimum noise adaptation of an amplifier to the antenna will be considered (wideband optimization).

Figure 1.8 shows both cases of interest.

-e-

ampli f ier

".O

(b)

Figure 1.8 Circuits for wideband SNR optimization. (a) Loop antenna.

(b) Whip antenna.

-e-The SNR at the input of the amplifier will be determined for the loop antenna, assuming a bipolar transistor as the first active device of the amplifier. Finally the resulting expression will be compared with expression (1.10).

First the optimum noise adaptation to the inductive source must be determined (figure 1.8-a). For a large part of the frequency band

of interest the spectrum of the equivalent noise current in e at the

input of the amplifier can be approximated by (see chapter 2)

S (Ir

(log)

4kl

2h FE'

Figure 1.9 Spectrum of the equivalent input noise current source for a bipolar transistor input stage with a loop antenna.

The bias current of the transistor determines the frequency <ox

where the spectrum will remain constant as a function of frequency. If wa assume the base resistance rb to be much smaller than re, the

value of re necessary to obtain a corner frequency of the noise spectrum at «x is

The maximum SNR for wideband optimization (SNRW) will be obtained

for frequencies higher than wx. It is given by

SNR„ ' hrr (1.11)

where the expression for re x has been used.

The SNR for selective SNR optimization (equation (1.10)) and the SNR for wideband SNR optimization (equation (1.11)) have been determined and can be compared to eaeh other.

The ratio of both SNR expressions is equal to (f > fx) SNRV =

SNRS

fx-Af

1.5-t~P (1.12)

In case of the receiver of interest, covering the frequency range of 150 kHz through to 30 MHz, the corner frequency is chosen equal to the low frequency band-edge of the SW band (* 2 MHz) as a compromise of an acceptable noise spectrum over the entire band. According to the definitions of fr and Af the frequency fr = 2.1

MHz and Af * 30 MHz. Thus for this receiver fx * fr and equation (1.12) can be approximated by

SNR

SNR

r* /rar-

(1

-

13)

Substituting the values of fr and Af in (1.13) results in

S W R" * 3 (1 14)

SNRS J u.i<*>

for frequencies higher than fx.

Although the calculations are performed for the loop antenna the situation with the whip antenna is similar and exactly the same

result (1.12) is obtained. In this case also a corner frequency fx

is present and when fx is chosen equal to fr again SNRW/SNRS * 3.

An important conclusion can be deduced from these results for the case of a reactive source irapedance, with a bipolar transistor as input device; for wideband receivers optimum noise adaptation will be obtained if the source is connected t£ the amplifier of the front-end.

This result is independent of the value of the source impedance as long as this impedance is reactive.

If field-effect input devices are considered it turns out that no

noise spectrum independent of Z0(s) can be obtained for the

selective SNR optimization but the same final conclusion is obtained as for bipolar transistors.

If only (high frequency) NPN transistors are available then, within the constraints of a limited supply voltage, it is rather difficult to realize an amplifier with a fixed input impedance and a current or voltage output [1.14]. If the impedance is realized by means of a single resistor then the SNR of the filter plus resistor, foliowed by an amplifier, will be worse than given by equation (1.8).

1.5.2 Other considerations about the front-end

In the previous subsection it was shown that for optimum noise performance the source should be connected to an amplifier and not to the image and spurious filter. Because the front-end must be able to handle large rf input signals, a limited value of the supply voltage means that the signal gain within the front-end will be limited due to the maximum allowable signal swing across the filter and across feedback impedances. This implies that the noise of the front-end also depends on the noise generated by the circuits following the amplifier.

parts of the front-end will be discussed, as well as a few other relevant aspects.

Because the filter is placed behind the amplifier, the only demands put on the filter concern the cut-off frequency and the order necessary to give sufficiënt rejection of the image channel and other spurious channels. The order of the filter also depends on the value of the chosen IF frequency; the higher the IF frequency, the lower the order of the image and spurious filter, to obtain a certain specified rejection of the image channel and other spurious signals.

All element values of the filter can be scaled to meet certain specifications. For instance we can choose a filter terminated with only one real impedance, and this real impedance can be placed at either the input or output of the filter. The value of the resistor can be chosen in accordance with noise and signal-swing

considerations. Of course the optimum solution is to realize the real impedance by means of a feedback amplifier with non-energetic feedback.

The output of the filter must be connected to a mixer. A current-switching mixer is the best circuit as far as noise and distortion performance is concerned [1.5]. Here the input quantity is a signal current.

The mixer must be driven by a periodic signal (the local oscillator signal). This can be realized by an harmonie oscillator [1.15] or a regenerative circuit [1.16]. To minimize the noise and distortion contribution of the mixer circuit (Chapter 3 ) , the mixer must be switched as fast as possible and this can be achieved by making the slopes of the oscillator signal at the zero crossings as large as possible. In practice the driving signal should preferably be a square wave, which can be obtained by limiting the output signal of an harmonie oscillator.

In practice it will always be necessary to place a buffer (limiter) between the local oscillator and the mixer to prevent interaction between the output of the mixer and the oscillator signal

("pulling"). Another important parameter of the switching signal of the mixer is its phase noise. If the phase noise of the signal is too large, a large unwanted rf signal, adjacent to the desired small rf signal, can "mask" the converted desired channel due to the phase noise of the oscillator signal (reciprocal mixing) [1.5]. This reciprocal mixing deteriorates the selectivity of the receiver because small rf signals can only be detected if undesired large rf signals are far enough away from the desired signal.

(log) (log) local oscillator L° f (log) (log) corwers ion > desired channel unwantccl . v j j a c e m channe i fr a fr u f (l 0g )

Figure 1.10 Example of reciprocal mixing.

&u-éL

fiF f (log)

The output of the mixer is conn which usually consists of one o In practice, due to the limited resistances of the resonators w the receiver. If the IF filter series-resonators (chapter 4) d mixer, the values of the loss r maximum signal swing for a eert voltage. Both the signal swing increasing value of the loss re to conform with the permitted p

ected to the IF bandpass filter r more mutually coupled resonators.

gain in the front-end, the loss ill also contribute to the noise of is made of one or more (coupled) riven by the output current of the esistances also determine the ain given value of the supply and the noise increase with an sistances which thus must be chosen ower consumption.

1.6 General considerations about the distortion

Not only the dynamic range of the front-end is an important figure of merit: the distortion performance must also be taken into account. In an upconversion receiver the complete rf band of interest must be handled by the front-end which, to maintain a sufficiënt selectivity, must be extremely linear. This, and noise considerations, are the main reasons why only a passive image and spurious rejection filter and a passive (first) IF band-pass filter can be used.

A figure of merit for the linearity of a circuit is its

intermodulation (IM) distortion. If two sinusoidal signals with equal amplitudes but different frequencies are applied to the circuit, the output signal of the circuit will contain distortion products at the sum and difference of the applied frequencies;

input : at output: n>(üi ± m-a2 with n,m integers The IM distortion is defined as the modulus of the ratio of one of the distortion components at the output to one of the desired frequency components at w, or co2 at the output.

Only mild non-linear systems are under consideration so that only frequency components at at ± w2. 2<>>i ± "2 and 2<y2 ± <v>i have to be taken into account. These are the frequency components generated by the second and third order distortion of the transfer. The

components at ui ± <o2 are generated by the second order distortion of the transfer while the components at 2ot ± w2 and 2(i>2 ± &>, are generated by the third order distortion of the transfer.

If U(CJ) represents the spectrum of the output signal of a circuit,

the IM2 distortion is defined as

IM2 =

0(&>i ± o2)

~üTó>7r

and the IM3 distortion is defined as

IM3

U(2(Ji ± C J2)

~üTwiT

U ( 2 < a2± M i ;

~vTö

T

U(u2) can also be chosen instead of IKw,).

Generally the IM2 and IM3 distortion of a circuit are frequency dependent since the signal transfer of the transistors and other reactive elements within the circuit are frequency dependent. In general a quantitative determination of the IM distortion of a circuit as a function of frequency is rather involved. In chapter 3 a quantitative description of the IM distortion will be presented for a differential pair used either as an AGC stage or as a switching mixer and in appendix 1 the IM distortion of a negative feedback amplifier is analyzed.

The value of the IM distortion of a circuit depends on the value of the input signal. If the non-linear transfer can be described by a Taylor series up to the third order an increase of the input signal

by 6 dB gives an increase of 12 dB of the IM2 distortion components

and an increase of 18 dB of the IM3 distortion components.

The signal-to-noise ratio (SNR) and the IM distortion are related to each other by means of the intermodulation free dynamic range

(IMFDR) of the circuit. The IMFDR is defined as the value of the SNR at the output at which the value of the IM distortion component equals the value of the noise (measured in a certain bandwidth). The IMFDR can be determined for the second order and third order

d i s t o r t i o n (IMFDR2 and IMFDR3, r e s p e c t i v e l y ) . F i g u r e 1.11 shows a t y p i c a l i n p u t - o u t p u t r e l a t i o n of a c i r c u i t . IM2 component IM3 component f r e q u e n c i e s of i n p u t s i g n a l s : 411, U2 Output components: IM2: (üj +W2 I M3: 2oii-ü2 Noise bandwidth: B IN (dB) Figure 1.11 Diagram of the IMFDR of a circuit.

One must bear in mind that the resulting IMFDR2 and IMFDR3 are

frequency dependent. The frequencies of the input signals necessary to determine the various quantities should be chosen close to each other. The noise floor at the output is usually determined in a specified bandwidth.

According to figure 1.11 the following relations between the IMFDR and the values of SNR and the IM distortion at an arbitrary output level can be deduced

IMFDR2 IMFDR3 = SNR - IM, 2-SNR - IM3 (1.16a) (1.16b)

with SNR and the IM distortion expressed in dBs.

For the receiver of interest the noise should be measured in a bandwidth of 2.5 kHz at the detector (SNR) and in a bandwidth of 5 kHz in front of the detector (CNR). Typical values of the IMFDR for a receiver are an IMFDR2 of 80 dB and an IMFDR3 of 100 dB.

The preamplifier and the mixer of the front-end must both have at least the desired IMFDR of the receiver. When the preamplifier is a

negative feedback amplifier, enlarging the loopgain of the

amplifier can decrease the distortion to a certain specified value (appendix 1 ) . However, no overall negative-feedback can be applied to the mixer. This implies that in principle the front-end can be designed such that the non-linearities of the mixer will determine the distortion performance of the front-end. Nevertheless other considerations, as for instance, a limited power supply, will limit the possibilities of practical realizations based on the above stated rule.

1.7 Discussion

In this chapter the architecture of a short-wave upconversion receiver front-end has been discussed. This architecture is chosen because it is well suited for monolithical integration, whereas the front-end of a downconversion receiver architecture is not.

Severe demands are put on the noise and distortion performance of the various parts of an upconversion receiver front-end.

The noise production within the various parts of the receiver determines its sensitivity and dynamic range. It has been shown that for an optimum noise performance of a wide-band upconversion receiver the first part of the front-end should exhibit an

amplifier connected to the antenna. Because an optimum noise

adaptation of this amplifier to the antenna is very important for a maximum sensitivity of the receiver, chapter 2 will be devoted to this subject.

Also the distortion performance of the front-end is an important figure of merit. Distortion, which is generated before channel selection has taken place, degrades the selectivity of the

receiver. Since the front-end must handle the entire dynamic range, the signal transfer of the active circuits must be extremely

linear. Negative-feedback can be used to linearize the transfer of the input amplifier (see appendix 1 ) , but overall feedback cannot be applied to the mixer circuit. Thus the distortion of the mixer will usually dominate and in chapter 3 the frequency dependent IM distortion performance of mixers and AGC circuits will be

discussed.

The IF frequency of the short-wave upconversion receiver is chosen about three times higher than the highest rf frequency of interest

(fir =» 100 MHz), and problems arise in realizing a channel

selective bandpass filter at this frequency. The relative bandwidth of the IF filter must be very small (* 1 0 ~4) . Lumped-element filters cannot be used at these frequencies for realizing a stable filter with the desired relative bandwidth because of component tolerances, losses and lack of the desired temperature stability. Quartz buik-wave resonators are not very attractive at these

frequencies because their fundamental resonance lie much lower than 100 MHz and additional components are necessary when using these resonators at their overtone resonances.

A solution is found by using surface acoustic wave (SAW) devices. Chapter 4 describes the design of Surface Acoustic Wave resonators on the piezoelectric material quartz.

References

[1.1] H.C. Nauta, "Fundamental aspects and design of

monolithically integrated AM radio receivers", Ph.D. thesis, Delft University of Technology, faculty of electrical

engineering, electronics research laboratory, the Netherlands, 1986.

[1.2] J. van der Plas, "Synchronous detector for an integrated AM radio receiver", Ph.D. thesis, Delft University of

Technology, faculty of electrical engineering, electronics research laboratory, the Netherlands,to be published in September 1990.

[1.3] L.K. Nanver, "High-performance BIFET process for analog integrated circuits", Ph.D. thesis, Delft University of Technology, faculty of electrical engineering, electronics research laboratory, the Netherlands, 1987.

[1.4] L.K. Nanver, E.J.G. Goudena, "Design Considerations for Integrated High-Frequency P-Channel JFET's", IEEE

Transactions on Electron Devices, vol. 35, no. 11, November 1988, pp. 1924-1934.

[1.5] See reference [1.1], chapter three.

[1.6] J. van der Plas, "Fasevergrendelende lus met lusversterking - en nulpuntscompensatie", patent pending, December 1988, the Netherlands.

[1.7] H.C. Nauta, E.H. Nordholt, "Fundamental aspects of noise optimization in radio input stages", IEEE Symposium proceedings of the 27th midwest symposium on circuits and systems, June 1984.

[1.8] See reference [1.1], chapter two.

[1.9] E.H. Nordholt, "Design of high-performance negative-feedback amplifiers", Elsevier Scientific Publishing Company,

Amsterdam, 1983.

[1.10] P.T.M. v. Zeijl, "Negative-feedback amplifiers with accurate input- or output-impedance in combination with high- or low-output- or input-impedance", patent pending no. 8701026, April 1987, the Netherlands.

[1.11] P.T.M. v. Zeijl, "Dual-loop negative-feedback amplifiers with impedance feedback suitable for monolithic

integration", Symposium proceedings of the 30th midwest symposium on circuits and systems, August 1987, pp. 925-928. [1.12] S. Seshu, N. Balabanian, "Linear network analysis", John

Wiley & Sons, I n e , New York, 1959, section 9.5.

[1.13] A.I. Zverev, "Handbook of filter Synthesis", John Wiley & Sons, I n e , New York, 1967.

[1.14] P.T.M. v. Zeijl, "A new high performance dual-loop amplifier", Proceedings of the 14th European solid-state circuits conference. Manchester, UK, 1988, pp. 150-153. [1.15] C.A.M Boon, "Design of high performance negative feedback

harmonie oscillators", Ph.D. thesis, Delft University of Technology,faculty of electrical engineering, electronics research laboratory, the Netherlands, to be published in

June 1989.

[1.16] C.J.M. Verhoeven, "The design of first order oscillators", Ph.D. thesis. Delft University of Technology, faculty of electrical engineering, electronics research laboratory , the Netherlands, to be published in November 1989.

2 NOISE OPTIMIZATION OF VARIOUS ANTENNA-AMPLIFIER

COMBINATIONS

Introduction

In the previous chapter it was demonstrated that in the case of a wide-band upconversion receiver the architecture of the front-end must begin with an amplifier to obtain an optimum noise adaptation to the antenna. The equivalent noise source at the input of the receiver is of importance because it sets an upper bound to the sensitivity of the receiver.

Therefore we will focus our attention in this chapter on the

optimum noise adaptation of the input amplifier of the front-end to an antenna. Although in practical receivers the equivalent noise sources of the circuits behind the amplifier usually also contribute to the equivalent noise at the input of the receiver, the noise optimization of the amplifier to the antenna is a first requirement for an optimum noise performance of the receiver. Noise optimization of the amplifier to the antenna can only be performed if the properties of the source are known, so we commence with a discussion of the properties of two antennas, the

electrically short whip antenna and the electrically short loop antenna. Although the whip antenna is normally used as a receiving antenna for short-wave receivers, the loop antenna is also

considered because it has some distinct advantages in environments where the receiving conditions for the whip antenna are poor.

2.1 The antennas

For the long-wave (LW) and medium-wave (MW) band a ferrite-rod antenna is normally used and a whip antenna for the short-wave (SW) band. The ferrite-rod antenna is sensitive to the magnetic field component of the incident electro-magnetic (EM) field, while the whip antenna is sensitive to the corresponding electric field. For the upconversion receiver, two types of antennas will be discussed: the loop antenna and the whip antenna.

A loop antenna can be used within environments where reception of the electric field is impeded by shielding or disturbances, as can be the case for example within buildings. Here also many electric spurious signals can be present and the reception of the magnetic field can often be used advantageously. It is convenient to use only one loop antenna for the reception of the entire rf band through to 30 MHz, so no core material will be used due the losses introduced by a ferrite rod at frequencies beyond a few MHz.

The other antenna type we will consider is a conventional whip antenna. Most portable receivers can also receive the FM band and whip antenna is used for this purpose around its series resonance frequency, implying an antenna length of about 0.7 m. The sarae antenna can also be used for the reception of the radio frequency

(rf) band through to 30 MHz.

2.1.1 The whip antenna

For the frequency range of interest, 150 kHz through to 30 MHz, the length of a practical whip is always short compared with the

wavelength (an electrically short antenna). As long as the length of the whip (h) is short compared to the wavelength X of the

incident waves of interest the antenna impedance will be capacitive while the radiation resistance is negligibe. The value of the capacitance of the whip is related to its length and the radius (a) of the whip. For a whip above an infinite perfectly conducting plane, and assuming h/A. < 0.25 and h » a, the following relation is valid [2.1].

Ca =

27T£0h

ln(£> - 1

(2.1)

where c0 = 1/(36n) • 1 0- 9 F/m is the permittivity of vacuüm.

The electrically short whip antenna converts the electric field component of the incident EM-field into a voltage independent of frequency. The relation between the voltage and the electric field is [2.1]

Ua = j-h-Ei, (2.2)

where Ua is the antenna voltage and Ej the component of the

incident electric field in parallel with the whip.

Figure 2.1 shows the antenna and its equivalent electrical circuit.

2a

2a

_ ^

O

2.1.2 The loop antenna

A loop antenna is sensitive to the magnetic field component of the incident EM-field. A time varying magnetic flux enclosed by the antenna induces an EMF (Uj„d) in the loop. Assuming harmonie excitation and expressing the induced voltage as a function of the electric field, the expression becomes

Uind

= - i

M L .

, (2.3)

where N is the number of turns, A the area of one turn and Zk the characteristic impedance of free space as defined by

Z

k

= (-£_] ,

(2

.4)

with Vo = 471-10 H/m. The impedance Zk is equal to 120-71.

As long as the total length of the wire U ) of the loop antenna is small compared to the wavelength of the incident field (an

electrically small loop antenna), the impedance of the loop antenna is inductive and virtually no radiation resistance will be present.

However the resistance (ra) of the wire can give an important

contribution to the antenna impedance. This resistance can be modelled as a loss resistance in series with the antenna

inductance. The value of the loss resistance is frequency dependent due to the skin effect. If the antenna consists of more than one turn (N > 1) the distributed capacitance of the coil must be taken

into account and can be modelled as a lumped capacitor (Ca) between

the two antenna leads.

A single-turn loop antenna and the equivalent circuit of the electrically small loop antenna are depicted in figure 2.2.

The admittance of the loop antenna is given by

Y

* =

J

*

+

-rrnsü

(2

-

5a)

where L

is the self-inductance of the antenna, r

the loss

resistance of the inductor and C

the parasitic capacitance of the

antenna. As long as

_uLa

r

then

(2.5b)

Y

* j*C

- ^ j —

-Jfe-r . (2.5c)

The last term of (2.5c) represents the losses of the coil. The

expression oL

/r

is usually called the quality factor (Q) of

the coil.

In case of a loop antenna the short-circuit current has a frequency

independent relationship to the incident EM-field. The

short-circuit current I

is given by, (assuming wL

/r

» 1)

Ii

»

- i s E T - " z ^ r

•

-

To determine the value of the short-circuit current, the inductance

of the loop antenna must be known.

From (2.6) an important conclusion can be drawn; a maximum value of

the short-circuit current of the loop antenna is obtained if the

factor NA/L

is maximized. In case of a single-turn loop (N=l),

with a predefined length of the wire, this implies that the area

must be maximized and the self-inductance minimized. A circular

single-turn loop is then the optimum solution. Also the parasitic

capacitance C

is minimum for such a loop.

The inductance of a single-turn circular loop can be expressed as

[2.1], (assuming r » a

)

Mo-t- [lnC-57-O "

] -

-

»

where r and ai represent the radii of the loop and the wire,

respectively.

If such a loop is used as an antenna and we denote the

circumference of the loop by

i , thus

then expression (2.7) can be rewritten for all practical situations

as

Ll

-_£_.<. [

l n

p £ ] - x ] .

(2

.

8b

,

Note the resemblance between expression (2.1) and (2.8b).

If the antenna consists of a number of circular turns close to each other, an approximation of the inductance is given by [2.2]

La

= _ , éfdÜ* . . , (

.9)

1- Il + 0.9--1J- - 0.02

fel '

as long as r/l < 30, where 1 is the length of the coil and r the radius of a loop.

One must bear in mind that a loop antenna is sensitive to the magnetic field component perpendicular to the area of the loop(s); the sensitivity will be zero if the magnetic field component of the incident magnetic field is in parallel with the area of the loop.

2.2 Definition of two reference antennas

In order to make a fair comparison possible between the signal-to-noise ratios (SNR) of various combinations of antennas and amplifiers, two "reference antennas" will be defined.

One antenna will be an electrically short whip and the other an electrically short single-turn circular loop. To obtain similar characteristics the antennas will be given the same electrical length. Thi.s implies that for an incident EM-wave the antennas behave in similar but dual fashion because the first resonant frequency of a whip corresponds to an antiresonant frequency of the loop.

The electrical length of a whip antenna (§y*) is defined as [2.1]

§w = 0'h , (2.10a)

and the electrical length of the loop antenna ($L) can be expressed

as

H Is the wave-number and is given by

e

= _^_ = _?J_ , (

.100

where c is the velocity of light, 3.108 m/s and X the wavelength.

Both antennas have their first resonance if the electrical length is equal to rc/2.

According to expressions (2.10a) and (2.10b) the electrical length of the antennas is the same when

i = 2-h . (2.11)

For a fair comparison not only the electrical length must be the same but also the radius of the wires must be equal, thus a = ai. In practice the radius of the whip will be larger than the radius of the wire of the loop antenna, so our reference antennas will nevertheless have different values of a and ai.

The reference whip antenna:

The reference whip antenna is a metal rod of 0.7 m length with a radius of 2-10" m. According to (2.1) the capacitance of this antenna is Ca = 8 pF.

The reference loop antenna:

The reference loop antenna is a circular loop with the same electrical length as the reference whip antenna; according to

(2.11) we have £ = 1.4 m. This corresponds to a radius of the loop

of 0.22 m and an area of 0.15 m2.

If we assume the radius of the wire (ai) equal to 0.5-10" m then,

according to (2.8), the inductance La of the loop is about 1.7 /uH.

The parasitic capacitance for this single-turn loop is assumed to be 0.5 pF.

A single-turn loop with a radius of 0.22 m can hardly be used in practice but a close approximation can be obtained by using a few widely spaced turns with a total wire length of 1.4 m.

2.3 Noise adaptation of the antenna to the amplifier

In chapter 1 it has been shown that for an optimum signal-to-noise ratio of the short-wave receiver the antenna must be connected to the amplifier. In this section the optimum noise adaptation of the input amplifier to the antennas will be determined.

For an optimally designed negative-feedback amplifier the equivalent noise sources at the input of the amplifier are about equal to the equivalent noise sources of the first active device of the amplifier [2.3]. In the subsequent sections we assume this to be the case. The input stage of the amplifier is assumed to be a

common-emitter or a common-source stage.

2.3.1 The reference transistors

In addition to the reference antennas as defined in section 2.2 we will define a reference bipolar transistor (BJT) and a reference junction field-effeet transistor (JFET). Their characteristics represent those of a typical integration process. The reference transistors will be used in the examples throughout this chapter. The reference BJT:

This reference transistor has the following parameters. hrE = 80 = 100,

rb = 50 O, TF = 8-10"11 s, C J E = C J C = 0.5 pF.

The DC common-emitter current gain is represented by IIFE, the small-signal current gain 80 is assumed equal to IIFE, while -rF represents the finite transit time of the transistor. At high currents where the junction capacitances C J E and C J C can be neglected compared with the diffusion capacitance the cut-off frequency wT of the transistor is about equal to 1 / TF.

The reference JFET:

W T = 2.5-10 radians/s, c = 1.5.

The constant c is necessary for the determination of the noise sources of the JFET.

The cut-off frequency oT of the JFET is defined as « T = gm/CiSS- If

the transconductance is known the input capacitance C,s s of the

JFET can be determined.

Considering a loop- and a whip antenna in combination with either a BJT or a JFET as an input device of the amplifier, gives four combinations which will be discussed below.

2.3.2 Whip antenna and bipolar transistor

This situation has already been described by Hauta [2.4], but for completeness the results are summarized. Figure 2.3 shows the circuit with the noise sources of interest.

Assuming that I Za I » rb and a « UT//hFE where &>T is the common-base cut-off frequency of the current gain, the spectral density of the equivalent input noise voltage source at the input of the amplifier is given by

where CT = Cb e + C J C w i t n cbe representing the sum of the

diffusion capacitance and the junction capacitance of the base-emitter junction. intr ins ie transistor

Ó^nc

= >

"■O

-e-Figure 2.3 Transformation of the noise sources of a bipolar transistor/whip-antenna combination to an equivalent input noise voltage source.

The small-signal emitter resistance re is given by

= k T = VT

r e qic ie '

where k is Boltzmanns constant (1.38-10 J/K),_T the absolute temperature, q the charge of an electron (1.6-10 C) and Ic the

collector bias-current of the transistor.

Usually the antenna capacitance Ca will be larger than the capacitance C T and expression (2.12) can be approximated by

S(U„ 4kT

₍

r

> * ? *

T E F I Ï W

] •

(2

-

13)

Figure 2.4 shows an example of the equivalent noise spectrum for two different values of re.

s (U 4kT (nb+ -j 4kT FE' e1 e2 u (log)

Figure 2.4 Spectrum of the equivalent input noise voltage of a bipolar transistor input stage with a whip antenna.

The minimum value of the noise spectrum is given by

S(Une q) . = 4kT[rb + -I5-} - (2.14)

H m i n *- L J

and is obtained for frequencies higher than the corner frequency <ax, which, according to figure 2.4 and expression (2.13), is given by

u

* = 2—^-JK—r •

-

From figure 2.4 it can be deduced that a compromise in bias current must be found to obtain an acceptable noise spectrum over the entire rf band of interest.

In practice the base resistance can usually be neglected compared with the emitter resistance re.

For a given corner frequency ux and neglecting rb, the minimum

noise spectrum for frequencies higher than a>x can be expressed as (according to (2.14) and (2.15))

S(U„eq) . = 4kT- . ^ , . (2.16)

The signal-to-noise ratio (SNR) is defined by

SNR =

/S(Une q) '

where a noise bandwidth of 1 Hz is assumed.

According to (2.2) and (2.16) a maximum value of the SNR is given by

SNRm a x = JillÜëïiilÜtE Ei . (2.17)

2.3.3 Whip antenna and a JFET [2.4]

Figure 2.5 shows the equivalent circuit and the noise sources of interest in case of a JFET.

"■O

Ca un e q

o

whip-antenna combination to an equivalent input noise voltage source.

The noise spectrum of the equivalent noise voltage source at the input is (neglecting the induced gate noise.)

S(Un ) eq

4kT 1 + 2qlc

o^ÖP

where c is a constant, with a value between 1 and 2 [2.5], gm is

the transconductance of the FET and Cj: gm/"r -g d • ^g s

is the gate-source capacitance and Cg d the gate-drain capacitance of the FET.

IG represents the gate leakage-current of the junction FET. In many cases this current can be neglected. Assuming this to be the case here, a minimum value of the noise spectrum can be found.

According to (2.18) and the relation C jS S = gm/wx the optimum value of C;s s is

C i ss , = Ca,

o p t

corresponding with an optimum value of gm given by

gE

o p t « T ' C a (2.19)

The spectral power density of the equivalent noise voltage source at the input is for this value of gm

S(Un )o p l eq 4kT-c-9mo p t (2.20) with gm o pt given by (2.19).

If the gate leakage current can be neglected then the noise

spectrum of the equivalent input noise voltage is constant over the entire frequency range of interest.

The SNR for this combination is independent of frequency due to the white noise spectrum. The maximum value of the SNR, according to

(2.2) and (2.20), is equal to

SNR

=

, (2.21)

4-/4kT-\/c~^ for a noise bandwidth of 1 Hz.

2.3.4 Whip-BJT versus whip-JFET

A comparison will be made of the minimum value of the noise spectrum of the combination whip - BJT with the noise spectrum of the whip - JFET combination. We will make use of the reference whip antenna as defined in section 2.2 and the reference transistors as defined in section 2.3.1.

In the case of the bipolar transistor we choose the corner frequency ux of the noise spectrum to be at 2 MHz (figure 2.4).

This gives an acceptable noise level over the entire frequency range of 150 kHz through to 30 MHz.

According to (2.15) the emitter resistance re must be equal to 1000 Q. The minimum value of the noise spectrum for this value of re is,

(according to (2.14))

S(Une q) = 4kT-550

H b i p

In the case of the JFET the minimum noise spectrum is obtained if the input capacitance C is s of the transistor is equal to the

capacitance of the whip, thus 8 pF.

The optimum value of the transconductance of the JFET is 20 mA/V and the value of the equivalent noise spectrum is (according to

(2.20))

S ( U ne q)J F E T = 4kT-300

Comparing both results shows that the JFET will obtain a better noise performance than the bipolar transistor. But a

transconductance of 20 mA/V can only be obtained by a JFET with a very large geometry and at the expense of a high bias current.

2.3.5 Loop antenna and a JFET

Because the short-circuit current of the loop antenna is the frequency independent quantity of interest, the equivalent noise current at the input will be determined. The antenna impedance will be modelled according to figure 2.2.