W e begin by examining the properties o f a simple 2 FET system. W e consider the case where we have two MESFETs with a width ratio w (Fig 7.1a). The drain currents are subtracted from each other. The wider main MESFET is held at a fixed bias, the secondary MESFET has an adjustable bias. We note that the 2nd and 3rd order derivatives o f a typical MESFET tend to peak near pinch o ff and drop as the channel is opened. If the main MESFET is biased further away from pinchoff than the secondary MESFET, there may exist a bias for the secondary MESFET when either the 2nd or 3rd order distortion products are cancelled.
This scenario was explored in a numerical package using derivatives from the Parker Skellern model o f a MGF1400. W e assume here that the dominant distortion products are from the transconductance nonlinearity (i.e. the load resistance is very small). Under such circumstances, when the sum o f the transconductance derivatives tend to zero, the
V/ w V;, bias2 biasl (a)
rHhr^
kdH
Vu;- (b)F ig 7.1 (a) T he sim p lified 2 F E T system (b) M o d ifie d form .
distortion w ill also tend to zero (hence the log o f the absolute value o f the derivative correlates directly with gain and intermodulation distortion on a dB scale). W e show the effect o f the adjustable bias on this system for two width ratios, w in Fig 7.2.
For very small widths w, the secondary MESFET has a negligible influence on the main MESFET. As the width increases, there exist bias points where shallow nulls (with respect to gate bias) begin to form (Left hand side o f Fig 7.2). These occur where the peak o f the derivatives o f the secondary MESFET are just under the magnitude o f those o f the main MESFET. The 2nd and 3rd order peaks are close but not coincident (due to the integral relationship between g2 and gg). As width w increases, there exist a range o f voltages where the derivatives o f the secondary device exceed those o f the main device. Deep nulls in distortion occur on either side o f this region. The slope o f the derivative with respect to bias is steeper on one side than the other, the steeper slope yields a steep sided nuU, whereas the gentler slope leads to an extended null. A w ide deep null can occur if the peak in the derivative just skims the derivative o f the main MESFET. As the width is increased the gain o f the system falls. The wider null increases the level o f overlap between the 2nd and 3rd order distortion products, allowing significant simultaneous reductions (right hand side o f Fig 7.2). The width o f the nulls also reduces sensitivity to bias variations.
We now consider a modified form o f Fig 7.1a, where both MESFETs have adjustable bias and we constrain vbiasl=vbiasl» and the main MESFET has an offset Voffset from that o f the secondary MESFET (Fig 7.1b). It was noted that in the previous case, where the rate o f the change o f derivative with Vbias2 was gentle, wide distortion nulls were formed. When
gl dB
Vgs=-0.4 w=0.2
gl dB
Vgs=-0.4 w=0.4
-20 -20 -25 -25 -50 -55 ^5 •45 -50 -50 -55 -55 ■1.6 -1.2 -0.8 -0.4 0 0.4 -2.4 -2 1.6 -1.2 -0.8 -0.4 0 0.4g2dB
Vgs
g2 dB
-20 -SO ^0 -50 -50 -60 -60 -70 -70 •1.6 -1.2 -0.8 -0.4 0 0.4 -1.6 -1.2 -0.8 -0.4 0 0.4g3 dB
g3 dB
-20 -20 -30 ^0 -50 -50 -60 -60 -70 -70 -80 -80 -2.4 -2. -1.6 -1.2 -0.8 -0.4 0 0.4 -2.4 -2 -1.6 -1.2 -0 .8 -0 .4 0 0.4Fig 7.2 M a g n itu d e o f th e d isto rtio n for tw o M E S F E T s as th e g a te b ias o f the secon d ary FE T is varied w hilst th e m ain M E S F E T is h eld co n sta n t. By u sin g d ifferen t w idth ra tio it is p ossib le to p rod u ce n ea r sim u lta n eo u s 2nd and 3rd ord er d istortion n u lls.
Vbias 1 ^ d Vbias 1 track, both derivatives can have similar slopes with respect to Vbias2»
leading to regions o f extended distortion nulling, away from the pinch o ff region (Fig 7.3). At a simplistic level, ignoring frequency dispersion effects, the region o f extended distortion nulling can be thought o f as distortion nulling with enhanced dynamic range, since the same signal is applied to both MESFETs. In Fig 7.3 w e see there is a trade o ff between the dynamic range o f the linearised region and the gain reduction which was mentioned in Chapter 6 section 6.3.
gl dB Vbia,i=-1.2 w=0.2 gl dB Vu:„i =-0.8 w=0.4 gl dB V I = -0.6 w =0.4 .20 .20 .20 .25 .25 .25 .30 -30 -30 -35 -35 .35 -40 -40 -45 -45 -45 .50 .50 .50 -55 .55 .55 ■1.6 -1 2 -0.8 -0.4 0. 0.4 -2 4 -2. -1.6 -1.2 -0.8 -0.4 0. ■1.6 -1.2 -0.8 - 0 4 0. 0.4 g2 dB g2 dB g2 dB .20 2 0 20 2 0 -30 -30 -40 -40 2 0 2 0 2 0 20 20 20 -70 -70 -70 ■16 -12 2 .8 2 4 0 0 4 ■1.6 -1.2 2 .8 2 4 0 0 4 ■1.6 -1.2 2 8 2 4 0. 0 4 g3 dB g3 dB g3 dB 20 2 0 20 20 20 4 0 -40 -50 -50 20 20 20 20 -70 -70 -70 20 20 20 ■16 -12 2 .8 2 4 0 2 4 2 . -1.6 -1.2 2 .8 2 .4 0. 04 -1.6 -1 2 2 .8 2 .4 0. 0.4
F ig 7.3 U sin g a secon d ary M E S F E T to p rod u ce n ear sim u lta n eo u s 2n d an d 3rd o r d e r d isto rtio n n u lls.
The case o f Fig 7.1b corresponds to the simplest example o f the Synthesised circuits based on derivative superposition (Chapter 6), where w and Voffset were chosen for the best match to the ideal linear amplifier derivatives.
We now relax the constraint vbiasi=vbiasb allowing vbiasl and Vbias2 to be independent variables. In Fig 7.4 we present contour plots o f the composite g i, g2 and g ] with Vbiasl and Vbiasl- The darker regions correspond to low gain or low distortion, the lighter regions to high gain or high distortion. W e include the two limiting cases; when w = l and when w=0. When w = l both MESFETs exactly cancel each other whenever Vbiasi=vbias2> leading to a valley along this equality. w=0 corresponds to that o f a single MESFET. In between these two cases, a U shaped valley is seen in both 2nd and 3rd order distortion. One side o f the U is approximately on a 45° line corresponding with Vbiasl=vbias2'^Voffset- This corresponds to the region o f extended distortion nulling with improved dynamic range.
Composite g l Composite g2 Composite g3 u - 0 4 - 0 8 -1 2 -1 6 -2 -2 4 0 4 0 . -0 4 -0 8 - 1 2 0.4 1.2 -0 .4 0 J \ 0 4 0 . -0 4 -0 8 - 1 2 - 1 6 2 2 4 0 4 0 -0 4 -0 8 - 1 2 -1 6 2 2 4 0 4 0 . -0 4 -0 8 - 1 2 - 1 6 2
An optimum region exists where reasonable gain and good reduction o f both 2nd and 3rd order distortion can be obtained simultaneously whilst giving a large dynamic range with reduced distortion.
7 . 3 T est .Tig D escrip tio n
To verify the derivative superposition technique o f Chapter 6, the simplest possible demonstrator circuit was built using 2 discrete MESFETs from the same wafer. Additional degrees o f freedom were built into the circuit to allow comparison o f dynamic range with a single common source stage and a balanced common source stage, together with variable gate biases to give the freedom to explore regions o f operation outside o f the synthesis optimisation. We show the overall schematic o f the demonstration board in Fig 7.5.
The simplest possible case o f the synthesis technique is the linear law which can be implemented with 2 FETs (corresponding with Fig 7.1b). Normally the FET widths would be scaled, but this is not possible with discrete devices, so a fixed Pi section attenuator was used to scale the current o f the secondary device. Bias-Ts were used to bias each FET individually. A transformer hybrid was used to subtract the output currents.
A transformer at the input gave in and out o f phase signals for the synthesised and balanced topologies respectively. The input transformer gives a 6dB loss by virtue o f splitting the input power equally between the two FETs. A set o f PCB jumpers were used to switch between the three configurations. In the common source mode, the half o f the input transformer is isolated from the secondary FET by working into an isolated load, the output conductance o f the secondary FET is used to preserve ac conditions at the load. The Pi section attenuator is an asymmetrical design, looking towards the output it presents 5 0 0 to the FET, whilst looking towards the FET, it presents a 2 9 0 0 load to the hybrid, approximately equal to the FET output conductance. The isolated ports do not need to see the characteristic impedance o f the system. An isolating combiner was used to minimise stray feedback voltages from the other channel. The hybrid was constructed o f trifilar wire wound on a ferrite balun former (Fair-Rite 43-2402) with a 2:2:3 ratio to give an
DD B.T. b&s R FIN R FO UT B.T. B.T.