Common Mode Stability

A particular feature of fully balanced system s is the need for external

stabilization of the comm on m ode (CM) DC operating point [97]. This can be a serious problem in tuned OTAs of the type w here Gm is varied by m eans of tail current tuning [37,38,53, 88,94]. For the design presented, Gm is varied

w ithout altering the DC bias conditions in any way, allow ing a sim pler com m on m ode feedback (CMFB) circuit to be em ployed [96] and this circuit is show n in Fig 5.5.3-1.

Vdd

Vo o— *|^M 20a,^ I#— o Vo

?

D17

D24

2x M16a

2x M17a oVadj

Vss

Fig 5.5.3-1 Com mon Mode Stabilization Circuit

The buffered o u tp u ts from the OTA are applied to the long tail pair consisting of M20a,b whose source voltage is a m easure of the CM o u tp u t voltage. This DC voltage is level shifted and applied to the gates of the OTA tail current source transistors in Fig 5.5.1-1, thus stabilising the overall CM operating point of the system. N ote that the CM operating point of the system can be adjusted by m eans of the current source of the CM stabilization circuit (Vadj) as show n in Fig 5.5.3-1.

The fully balanced, differential OTA-C integrator is com pleted by the connection of an integrating capacitor betw een nodes x and y of Figs. 5.5.1-1 and 5.5.2-1 and as show n by Fig 5.5.3-2. The current sources are conventional single cascode arrangem ents [95].

V c q | M7aJL ' I M7b = i5 j0 = Rqp^ = 6oon Cp»,b =10 pF Vout- «L 2x M8b 2xM8a Rqsa Kqpa I Rqpb Rqsb +12.5V D13b M9a 6 D16b

?

2x Mob 2x M6a MlOa M13b M13a M12a M12b +2.5v 2x M4a I 2x M4b 1+ j - I—, , r * *—I - r-^ -1, >

• — M M 2a,b k — I I— H W 20a M 20b k I— Ml a , b k — •

' - ^ I r I

S

e

T

I ^ I r

I Vout+

Fig 5.53-2 Com plete Dual Input Fully Balanced OTA-C Integrator

5.6 Simulated Performance of OTA-C Integrator 5.6 1 Single-Ended OTA-C Integrator

The circuit of the complete OTA-C integrator is given in Fig 5.6.1-1. The effect of the double cascoding is to decrease the contribution of the OTA o u tp u t conductance Goa to the total o u tp u t conductance Go as

illustrated by section 5.4.1. This serves tw o m ain functions: firstly, since the o u tp u t conductance of the OTA is now very sm all (0.071 go at the extrem es of Gm tuning). Go is dom inated by the conductance of the bootstrap load Gol and hence increases the available Go tu n in g range for a given Rq. Secondly, varying the conductance of M l2 (to

im plem ent Gm tuning) has very little effect on the OTA o u tp u t conductance Go and hence the functions of Gm and Go tu n in g are effectively de-coupled, facilitating the design of sim ple control

circuitry. A lthough the presence of tw o levels of cascoding restricts the b a n d w id th of the OTA som ew hat, this is im m aterial since the overall ban d w id th of the system is dom inated by the load.

+15v Rqp Rqs +12.5V -— i - C I ÿ D - Vcq M6 M2 M5 +10v +10v M l M3 M4 M13 +5v M7 |M14 +2.5v C D :^ M 12 M i l MIO M8

Vin- Vin+ Vout

Vcf

+2.5v-

-2.5 V

Vbias -5V

Fig 5.6.1-1 Complete Fully Tunable OTA-C Integrator w ith Independent Control of Gm and Go

The o u tp u t current from the O T A /bootstrap load com bination is passed through the integrating capacitor Cl and the resulting voltage

buffered and level shifted to facilitate connection to the next stage. The o u tp u t buffer consists of the source follower M13, a diode string and an externally adjustable cascode current source, allowing DC offsets to be nulled. The excess phase contribution of the diode string is

com pensated by the bypass capacitor Co. The unity gain voltage buffers serve a dual purpose, enabling a DC level shift from the

transconductance point, loaded by Cl to the input of the next OTA-C,

and also providing a low im pedance o u tp u t allowing a num ber of 2nd order sections to be cascaded.

The load capacitor Cl w as chosen for a nom inal unity gain frequency

of 60MHz (CL=4pF). A lthough in theory the device w idths can be scaled to any required value, this should be kept as sm all as possible in order to m inim ise pow er consum ption. A device w id th of 20|im was used in the design, w hich is the m inim um w idth for w hich the foundry process is characterised.

5.6.2 Integrator Frequency R esponse w ith T uning

The frequency response of the OTA-C integrator w as sim ulated using the SPICE level 1 (jFET) m odel w ith param eters chosen for best fit to m easured foundry data for a 20|X x 0.5p device. Figs 5.6.2-la & b show plots of the am plitude and phase of the AC frequency response w ith tun in g of the circuit of Fig 5.6.1-1.

Figure 5.6.2-la show s the variation in gain (ie., 40.2 to 88.4) achieved by controlling Go, w hile m aintaining Gm constant. This w as obtained by varying Vcq-12.5V (nom inal value: -0.6V) in the range: -0.28V > Vcq- 12.5V > -0.74V. N ote th at the unity gain frequency rem ains unaltered at 60MHz u nder this variation of Go. Figure 5.6.2-lb show s the

variation of the unity gain frequency (ie., 45MHz to 70MHz) achieved by controlling Gm, w hile m aintaining Go constant. This w as obtained by varying Vcf-2.5V (nom inal value: -0.6V) in the range: 0.6V > Vcf- 2.5V > -IV. Note that in this case the gain also varies since this is a function of both Gm and Go. Both figures show the excess phase due to the finite b an d w id th of the OTA.

In addition, by w ay of a com parison the fully balanced version w as also sim ulated to show th at none of the tuning behaviour of the single­ ended version w as lost. The AC frequency response w ith tuning of the circuit of Fig 5.5.S-2 is show n by Figs 5.6.2-2a & b.

40 40 20 -40 o -80 -2 0 -1 2 0 -40 -160 -60 frequency (Hz)

Fig. 5.6.2-la Single-Ended A m plitude & Phase Response of the OTA-C Integrator (Gm constant. Go varied)

40 40 20 -4 0 cn -8 0 -2 0 -1 2 0 -160 -6 0 -180 -80 frequency (Hz)

Fig. 5.6.2-lb Single-Ended A m plitude & Phase Response of the OTA-C Integrator (Gm varied. Go constant)

40 40 20 ^ 0 O) -80 -2 0 -1 2 0 -4 0 -160 -60 -180 -80 frequency (Hz)

Fig. 5.6.2-2a Fully Balanced A m plitude & Phase Response of the OTA-C Integrator (Gm constant. Go varied)

40 40 20 -40 O) CO T3 % -2 0 (C CD -80 CL -4 0 -1 2 0 -60 -160 -80 -180 frequency (Hz)

Fig. 5.6.2-2b Fully Balanced A m plitude & Phase Response of the OTA-C Integrator (Gm varied. Go constant)

5.6.3 Integrator D istortion w ith T u n in g

In assessing the total harm onic distortion (THD) of an OTA, a frequently adopted m ethod is to m easure the harm onic p u rity of the short circuit o u tp u t current in response to a sinusoidal in p u t voltage [89,94]. H ow ever, w hen the OTA is term inated by a capacitor as an OTA-C integrator for use in a state variable filter, the non-zero load im pedance allows an AC voltage to appear at the o u tp u t node w hich introduces additional harm onic distortion. In [98,99] a m ore com prehensive distortion test w as proposed w hich consists of the following set of three m easurem ents of the o u tp u t in response to a sinusoidal input:

(1) Short circuit o u tp u t current ('S /C );

(2) O u tp u t voltage w ith a resistive load of 1/G m ('1/Gm'); (3) O u tp u t voltage w ith load open circuit ('O /C )

M easure (1) is the traditional m ethod of evaluating the linearity of an OTA, effectively ignoring the load conductance Go. In m easure (2) the OTA is shunted w ith a resistive load (replacing the load capacitor) equal to the m odulus of the load im pedance of an OTA-C integrator at its unity gain frequency (ie., the centre frequency of a 2nd order state variable filter) and the o u tp u t voltage is m easured for non-linearity. M easure (3) is an extreme test in w hich the OTA is effectively em ployed as a voltage am plifier w ith the controllable Go serving as load providing a voltage gain of 30dB and as in the case of m easure (2) the am plified o u tp u t voltage is m easured for non-

linearity.

The AC am plitude frequency response of the OTA-C Integrator show n in Fig 5.6.1-1 are presented by Fig 5.4.2-2, and Fig 5.6.3-1 w hen connected as

required for tests 1,2 and 3 above. In all cases the integratingj capacitor Cl is disconnected. In the case of test (1), the frequency response of the OTA transconductance, Gm is show n in Fig 5.4.2-2 w hen subjected to tuning. For tests (2) the OTA is loaded in place of the integraing capacitance Cl w ith a resistance equal to 1/G m , giving a unity voltage gain, w hile for test (3) the

load conductance Go is varied w ith Gm tuning to

I

m aintain a voltage gain (G m /G o) of 30dB, as show n in Fig 5.6.3-1. 40 30 n: 20 \ v Gm Max — Gm Min -1 0 -2 0 frequency (Hz)

Fig. 5.6.3-1 Resistive Load (1/G m ) and Voltage Gain (30dB) Frequency Response (Cl=0)

In order to assess the linearity of the OTA, AC distortion m easurem ents w ere carried out w ith the circuit connected in the three configurations discussed above and w ith sinusoidal inp u ts of am plitude 500mV and lOOmV. Since the b an d w id th of the OTA is different in each configuration, the linearity tests w ere carried out at 10% of the nom inal -3dB frequency in each case so that the results w ere not affected by high frequency harm onic attenuation. As in the case of the b an d w id th m easurem ents, linearity w as m easured w ith Gm at the extremes of its range. The results are presented in Tables 5.6.3-1, 2 &3.

Single-Ended Gm (mA/V) TH D with output s/c @ IG H z, Single-Ended (%) TH D with output s/c @ IG H z, Fully Balanced (%) Fully Balancée Gm (mA/V) Vin=500mV (pk) Vin=100mV (pk) Vin=500mV (pk) Vin=100mV (pk) 1.99 1.68 0.32 1.09 0.03 8.03 1.64 1.31 0.20 0.75 0.03 6.63 1.29 1.41 0.19 1.01 0.04 5.09 (a) (b)

Table 5.6.3-1 : Total Harmonie Distortion of OTA Transconductance Gm (short circuit o u tp u t current) : (a) Single-Ended (b) Fully Balanced

Single-Ended Gm (mA/V) TH D with load= l/G m Vin=100mV(pk) @ 400M Hz, (%) 1.99 0.26 1.64 0.16 1.29 _0.12 THD with load = l/G m Vin=100mV(pk) @ 400M Hz, (%) Fully Balanced Gm (mA/V) 0.02 8.03 0.01 6.63 0.02 5.09 (a) (b)

Table 5.63-2 : Total Harmonie D istortion of OTA Voltage Gain (1/G m Resistive Load) : (a) Single-Ended (b) Fully Balanced

Single-Ended Gm (mA/V) THD with Gm/Go=60 Vo=500mV(pk) @ lOMHz (%) 1.99 2.36 1.64 0.96 1.29 6.25 THD with Gm/Go=60 Vo=500mV(pk) @ lOMHz (%) Fully Balanced Gm (mA/V) 0.21 8.03 0.15 6.63 0.44 5.09 (a) (b)

Table 5.6.S-3 : Total Harm onie D istortion of OTA Voltage Gain (Load O pen Circuit, Go) : (a) Single-Ended (b) Fully Balanced

The overall THD levels of the OTA, m easured u n d er a variety of conditions, are quite m oderate. If the peak signal level (input for tests 1 & 2, o u tp u t for test 3) is restricted to lOOmV (peak), the THD levels are at m ost of the order of 1%. O n the other hand, larger signal levels produce quite high levels of

THD, about 10% in some cases. If required, these levels can be reduced by em ploying source degeneration in the OTA. Alternatively, the use of the fully balanced version of the OTA, provides a m ore com prehensive solution to the reduction of THD levels.

5.7 Simulated Performance of Bandpass Filter 5.7.1 2nd Order CT Bandpass Filter

The proposed 2nd order bandpass section is show n in Fig 5.7.1-1. It consists of tw o O perational Transconductor-C amplifiers (OTA-C) of the type in Fig 5.6.1-1, configured as a tw o integrator loop giving a bandpass response.

V c f V cq V in 0- V in + O V o V in - Vin+ V in - bp

Fig 5.7.1-1 Fully Tunable 2nd O rder Bandpass Section

The OTA-C integrators w hich feature independent control of the

transconductance gain (Gm) and o u tp u t conductance (Go), enables high and variable DC gains to be achieved w ithout the use of separate transconductors configured as linear resistors [94,100]. For the case of high gain (ie low loss, thus high Q) the bandpass section exhibits good dc stability.

The 2nd order transfer function T(s) (ignoring excess phase shifts due to am plifier bandw idths) is given by equation (5.7.1.1):

Gm ^ Go^ s +

= * c T ' * — G —

For the case of high Q, w here Gm is m uch greater than Go, then the centre frequency Fq and Q can be show n to be governed by equations (5.7.1.2) &

(5.7.1.3):-

(5.7.1.2)

Q . g (5 .7 .1 .3 )

and so for Q < 30, we require that m axim um gain (G m /G o) < 60 (35dB).

5.7.2 B andpass Filter Frequency R esponse w ith T uning

The am plitude frequency response of the bandpass filter circuit of Fig 5.7.1-1 is show n by Figs 5.7.2-la & b.

The frequency response of Fig 5.7.2-la show s the tuning range of Q available w ith the application of a DC voltage varied -0.4V > Vcq-12.5V > -0.7V to control Go w hile m aintaining Gm constant (ie centre frequency 'Fq' rem ains

unaltered). The Q of the filter varies betw een 24 to 41.

The frequency response of Fig 5.7.2-lb show s the range of Fq available by the application of a dc voltage varied 0.6V > Vcf-2.5V > -IV controlling Gm

w hile m aintaining Go constant. N ote th at w hereas Q can be varied independently of Fq, variation of Fq also varies Q to some extent, since Q=(G m /2G o) to a 1st order. How ever, the independence of the Q control represents a considerable advantage in a system requiring autom atic adaptive tuning.

■S o 50 45 40 35 30 25 20 15 10 5 60 61 62 63 64 65 56 58 59 55 57 Frequency MHz

Fig 5.7.2-la Q Tuning Frequency Response (Gm constant : Go varied)

• i

Ü

Frequency MHz

Fig 5.7.2-lb also show s that the variation of Fq at higher frequencies varies Q in a non-linear m anner, (ie Q ^ G m /2G o), this is attributed to the finite b an d w id th of the transconductance amplifiers causing a degree of Q- enhancem ent, an effect w hich is present in all active filter realisations.

U sing this approach, a fully tunable, 2nd order bandpass filter w ith

independent control of centre frequency and Q has been realised w ith only

two OTA-C integrators.

5.7.3 T ransfer Function Accuracy

The design of the fully tunable 2nd order bandpass filter is intended to be one section of a 12th order bandpass filter providing a Transitional G aussian response centred at 60MFlz. This class of filter is required to exhibit both accurate am plitude and group delay responses. The effects of finite excess phase in all active filter designs w as explored in chapter three w ith a resulting specification on the required transfer function accuracy of a 2nd order bandpass filter. The am plitude and group delay responses of a 2nd o rder bandpass filter of Fig 5.7.1-1 using fully tunable integrators of Fig 5.6.1- 1 is show n by Fig 5.7.3-la & b.

As show n by Fig 5.7.3-la & b the am plitude and group delay responses of the 2nd order bandpass filter are very closely m atched to that of an ideal 2nd o rder response. To com pare the differences m ore closely, the error betw een the tw o am plitude and group delay responses are show n by Fig 5.7.3-2a & b.

As show n by Fig 5.7.3-2a the highest am plitude error of 0.7% occurs at the extrem es of frequency w hich is well w ithin the acceptable error of 2.2% [chapter 3, 3.4.2]. In addition, the group delay is also w ith the required error, increasing only to a m axim um of 3.5% at the extrem es of frequency

30

25

p 20

Ideal 2nd Order Response — Simulated 2nd Order Response

64 65 62 63 59 60 6 frequency (MHz) 56 57 55

Fig 5.7.3-la A m plitude Response of 2nd order bandpass Filter

180 160 140 120 60 40

20 Ideal 2nd Order Response — Simulated 2nd Order Response

55 56 57 58 59 60 61 62 63 64 65 frequency (MHz)

0.8 0.7 0.6 0.5 0.4 Q . 0.2 - 0.1 55 56 57 58 59 60 61 62 63 64 65

In document Design of a fully tunable gaas mesfet OTA-C integrator suitable for high-precision continuous-time filtering (Page 125-139)