1 S.A.Maas, Nonlinear Microwave Circuits, Artech House 1988, ppl3-16.
2 A.HAghvami, I.D.Robertson, "Power Limitation and High Power Amplifier Nonlinearities in On- Board Satellite Communication Systems", lEE Electronics & Communication Journal, Vol 5, No 2, pp65-70.
3 A. N. Thiele, “Measurement of Nonlinear Distortion in a Band-Limited System,” J. Audio Eng. Sac.,
1983, vol. 31, no. 5., pp 443-445.
4 J. B. Scott and D. Heuer, “A high performance total difference frequency distortion (TDFD) meter,”
Journal o f the Audio Engineering Society, vol. 42, no. 6, pp. 483-489, June 1994.
5 O. J. Ridler, “A radio frequency total difference frequency distortion (TDFD) meter,” BE Honours Thesis, University of Sydney, Dept, of Electrical Engineering, 1994.
6 A. E. Parker and J. B. Scott, “Intermodulation Nulling in GaAs MESFETs”, lE E Electronics Letters,
vol. 29, no. 22, pp. 1961-1962, October 28, 1993.
7 SA.Maas, A.Crosmun, Modelling the Gate I/V Characteristic of a GaAs MESFET for Volterra-Series Analysis, IEEE MTT Vol. 37, No. 7, July 1989
8 J. C. Pedro and J. Perez, “Accurate Simulation of GaAs MESFETs Intermodulation Distortion Using a New Drain-Source Current Model,” IEEE Trans, on Microwave Theory and Techniques, vol. 42, no. 1, pp. 25-33, January 1994.
9 Y.P.Tsividis, D.L.Fraser, Harmonic Distortion in Single-Channel MGS Integrated Circuits, IEEE Journal of Solid-State Circuits Vol. SC-16, No 6, December 1981, pp. 694-702.
10 E.Fong, R.Zeman, Analysis of Harmonic Distortion in Single Channel MGS Integrated Circuits, IEEE Journal of Solid-State Circuits Vol. SC-17, No 1, February 1982, pp. 83-86.
11 M T.Abuelma'atti, High Performance of Single-Channel MGS Integrated Circuits, IEEE Journal of Solid-State Circuits Vol. SC-20, No 4, August 1985, pp. 860-864.
12 S.A.Maas, Nonlinear Microwave circuits, Artech House 1988, pp. 156-172 (4.1).
13 S.Narayanan, Transistor Distortion Analysis Using Volterra Series Representation, The Bell System Technical Journal, May-June 1967, pp. 991-1024.
14 S .Narayanan, H.C.Poon, An Analysis of Distortion in Bipolar Transistors Using Integral Charge control Model and Volterra Series, IEEE Transactions on Circuit Theory, July 1973, pp. 341-351.
15 S.A.Maas, B.L.Nelson, D.L.Tait, Intermodulation in Hetrojunction Bipolar Transistors, IEEE Transactions on Microwave Theory and Techniques, Vol. 40, No. 3, March 1992, pp. 442-448.
16 S.A.Maas, Nonlinear Microwave circuits, Artech House 1988, pp. 172-207, (4.2).
17 E.V.D.Eijnde, J.Schoukers, Steady-State Analysis of a Peridodically Excited Nonlinear System, IEEE Trans Circuits and Systems, Vol. 37, No. 2, February 1990, pp. 232-242.
18 G.L.Chin, P.M.Lin, Computer aided Analysis of Electronic Circuits, Prentice Hall, 1975.
19 L.G.Chua, P.Lin, Computer Aided Analysis of Electronic Circuits: Algorithms and Computational Techniques, Prentice Hall 1975.
20 S A.Maas, Nonlinear Microwave circuits, Artech House 1988, pp. 81-153.
21 V.Rizzoli, A.Lipparini, A.Costanzo, F.Mastri, C.Cecchetti, A.Neri, D.Masotti, State-of-the-Art Harmonic-Balance Simulation of Forced Nonlinear Microwave Circuits by the Piecewise Technique, IEEE Trans MTT, Vol. 40, No. 1, January 1992.
22 K.Bult, Analog CMGS Square-Law Circuits, PhD Thesis, University of Twente 1988. pp. 22, 93-97, 197-202.
2 . 4 L ow F re q u en cy D esig n T ech n iq u es
In this section w e review a selection o f linear and nonlinear circuit design strategies appertaining to low frequency circuit design (IHz-lOM Hz). The purpose o f this section is to illustrate the abundant richness o f circuit design techniques available for CMOS and Bipolar whilst high lighting the comparative poverty o f the GaAs MESFET repertoire. This hints at the potential value o f the new design technique proposed by the author Chapter
6
.2 . 4 . 1 L in ea r C ircu its
2 . 4 . 1 . 1 O P -A M P C ircu its
The integrated form o f the operational amplifier (OP-Amp) has had a profound impact on the design o f circuits below about lOkHz. It provides a stable, easy to use building block from which all kinds o f linear and nonlinear circuits can be derived. Due to its integrability and its universal applicability, the operational amplifier is cheap and mass produced.
A simplified schematic o f an operational amplifier is shown in Fig 2.4.1a. It consists o f a differential pair input working into an active load (current mirror) and gives a high gain. This feeds into a common source stage, also with a current mirror load and a level shifter (vbe multiplier). Finally this is followed by a class AB buffer amplifier, giving power
V d d O O O u t Out Bias 2 0 —^ -ve Bias lO —) Inputs ■•O Vee +ve V ssO a
G ain=l+Zl/Z 2
Out (i)
Out (v) O—[
Out
gm =l/R
Vout=Vin G ain=Y2/Yl Gain(f)=FcUjCg/j2;rfCf
T ransZ =l/Y l
F ig 2.4.2 S elected O P -A m p C ircu its (a) N o n in v e r tin g A m p lifie r (filte r ), (b) T ra n sco n d u cta n ce (V oltage R egu lator) (c) In v ertin g A m p lifier (filter) and T ra n sim p ed a n ce (d) S w itch ed C apacitor F ilter
amplification and drive capability. The entire circuit is DC coupled. A frequency compensating capacitor is generally added to ensure stability under all feedback conditions. The DC open loop gain o f a typical OP-Amp is in the order o f lOOdB with a comer frequency o f around lOHz. The circuit is invariably used with strong negative feedback to give highly controlled gain, and reasonable linearity.
Many refinements have been made to the basic OP-Amp, including offset voltage reduction, noise reduction, FET input and BiCMOS implementations (to give very high input impedances) and various slew rate improvement strategies. To overcome the basic speed limitation o f the OP-Amp attempts have been made to design GaAs versions. The high output conductance o f existing GaAs MESFET processes have limited the gain achievable, and extensive cascoding is used, requiring large power supply voltages. Never the less, gain bandwidth products in the GHz region have been reported [1]. A typical single end input GaAs MESFET OP-Amp design is shown in Fig 2.4.1b.
In Fig 2.4.2 we show a collection o f common OP-Amp circuits, (a) shows the standard noninverting amplifier, which can be made into a filter by giving frequency dependence to
the feedback, (b) shows the transconductance amplifier w hose transconductance is
determined by the resistor. The same circuit is also be used extensively as a voltage regulator, by making the input a reference level and taking the output voltage across the resistor, (c) shows the inverting amplifier, which can be made into a filter by giving frequency dependence to the feedback. With a current input, the circuit behaves as a transimpedance amplifier, (d) shows the switched capacitor filter. A two phase clock is
^ d Vx=Vy Vx=Vy V x = V y
Iz=Ix
Vx=Vy
Iz=Ix
Vx=Vy ^
Iz=-Ix
Fig 2.4.3. A S electio n o f Im p lem en ta tio n s o f th e C u rren t C on veyor, (a) Sim ple C urrent M irror fo rm , (b) In v ertin g and N o n in v e r tin g O P -A m p Su pp ly C urrent S en sin g (c) S in gle M O S F E T form (d) T ra n slin ea r form based on W ilson C urrent M irror.
used. The first phase charges Cg. The second phase discharges Cg into the virtual earth input, charging Cf. The switching mechanism causes Cg to behave like a frequency dependant resistor. The frequency response is controlled by the ratio o f Cg and Cf and the frequency o f the switching. These simple building blocks are frequently assembled into more complex structures such as instrumentation amplifiers and BiQuad filter circuits etc. etc. etc.
2 . 4 . 1.2
C urrent M ode C ircu itsInterest in current mode electronics has flourished since the late 1980's when performance advantages over the reigning OP-Amp family began to be widely recognised. The origins
RI
oiiT In Out In (|)l Out
o— o— <- #---
^L /*'
sL f* ' s L f* '
GAIN=1+R2/R1 b J ? C J l
F ig 2 .4.4 (a) S im p lified C u rren t F eed b a ck O P -A m p , (b) C u rren t C o p ier C ell, (c) 2 C urren t C opier Cell co n fig u red as a d elay elem en t.
o f current mode electronics date back to 1968 to the idea o f the current conveyor proposed by Smith and Sedra [2]. Many different implementations have subsequently been proposed together with innumerable applications [3,4]. W e illustrate a selection o f current conveyor topologies in Fig 2.4,3.
The current conveyor allows amplifiers to be realised with a bandwidth largely independent o f the voltage gain being produced. The Y node o f the current conveyor behaves rather like the virtual earth associated with the OP-Amp inverting amplifier, with some versions making this a high impedance node and others making it a current carrying node. With this topology innumerable linear analogue functions associated with amplifiers and filters have been reported, together with the emergence o f commercial 1C designs.
There are two other classes o f linear current mode circuits which are also important. The first is an extension o f the basic current conveyor - the current feedback OP Amp (Fig 2.4.4a). Here a current conveyor works into an open circuit load followed by a buffer amplifier. The Y input provides a high impedance input and the X input allows current feedback. The second is the current copier cell [5,6] (Fig 2.4.4b), which can be considered as an analogue memory cell. On the first phase o f the clock the gate source capacitance o f the MOSFET is charged to a voltage that produces a current identical to the input. On the second clock phase the input is disconnected and the memory element is connected to its output, into which it drives the input current. By cascading these memory cells in an antiphase sequence (Fig 2.4.4c), analogue delay line can be made that transmits current (unlike the bucket brigade line, a charge coupled device). This delay line has been proposed as the basis for the Switched Current Filters [7,8].