Variable-transconductance four-quadrant Gilbert-type modulator with feedback circuitry in improved NMR transmission

A variable-transconductance four-quadrant Gilbert-type modulator comprises a differential-transconductance amplifier, a fixed current source, a current sensing resistor, variable-transconductance circuitry, and feedback circuitry. The feedback circuitry is operatively connected to the differential-transconductance amplifier and to the current sensing resistor to receive the modulation voltage signal and to cause the voltage across the current sensing resistor to follow the voltage of the modulation voltage signal thereby causing the differential output current of the differential-transconductance amplifier to be directly proportional to the voltage on its input port thereby improving the linearity of the modulator. Also provided is an isolation output amplifier on the modulated output of the modulator to improve isolation between the carrier input signal and the modulated output.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates, in general, to balanced modulators and, more 
particularly, to variable transconductance four-quadrant Gilbert-type 
modulators with improved linearity and improved carrier suppression. 
2. Description of Related Art 
Analog modulators and multipliers are well known. One particular type of 
well known multiplier circuit is a variable-transconductance four-quadrant 
differential-pair or Gilbert-type multiplier. Such circuits are designed 
for use where the output of the circuit is a linear product of two input 
voltages. Typically, the linear product is adjustable by a scale factor. 
The basic differential-pair multiplier was introduced in B. Gilbert, "A 
Precise Four-Quadrant Multiplier With Subnanosecond Response," IEEE 
Journal of Solid State Circuits, SC-3, No. 4, pages 365-367 (December 
1968). See also, Clarke et al., Communication Circuits: Analysis And 
Design (Addison-Wesley Publishing Co. 1971), pages 362-373, for a textbook 
treatment of the Gilbert-type multiplier. The four-quadrant Gilbert-type 
multiplier is readily available in integrated circuit form. For example, 
Motorola Semiconductors produces a four-quadrant multiplier chip known as 
an MC1595L chip. 
Where one input to the above-described variable-transconductance 
four-quadrant Gilbert-type multiplier is a carrier signal and the other 
input is a modulation input, the multiplier becomes a useful modulator. 
Such a modulator is commonly known as a balanced, suppressed carrier, or 
double sideband modulator as well as a variable-transconductance 
four-quadrant Gilbert-type modulator. Practical uses of these types of 
modulators include AM transmission and reception and generation of pulses 
of modulated radio-frequency ("RF") current in the transmission circuitry 
of magnetic resonance imaging ("MRI") systems (also known as nuclear 
magnetic resonance ("NMR") imaging systems). In the MRI system, the 
modulated RF current is used to generate an alternating magnetic field for 
the controlled excitation of the nuclei of the body being examined. 
A variable-transconductance four-quadrant Gilbert-type modulator is shown 
in block diagramatic form in FIG. 1 as element 10. Modulation input 
voltage A(t) is input into modulator 10 at modulation input port 11, and 
carrier input signal V.sub.c (t) is input at carrier input port 12. The 
resulting modulated output V.sub.out (t) is produced at modulated output 
port 13 of modulator 10. Contained in the modulator are 
differential-transconductance amplifier 14, two fixed current sources 15, 
current sensing resistor R.sub.1, and variable-transconductance circuitry 
16. Differential-transconductance amplifier 14 has input port 17 
consisting of two leads for receiving the modulation input voltage, has 
common port 18 for receiving drive currents from fixed current sources 15, 
and has output port 19. Differential-transconductance amplifier 14 
includes two active devices 20, 21 having their input (20A, 21A), output 
(20B, 21B), and common (20C, 21C) leads as shown in FIG. 2. Active devices 
20, 21 could be, for example, bipolar transistors in which the inputs 
(20A, 21A) are the bases of the transistors, the outputs (20B, 21B) are 
the collectors, and the common (20C, 21C) leads are from the emitters. The 
active devices could also be JFETs, for example, with the gates as inputs, 
sources as outputs, and drains as commons. 
The currents on the input leads to active devices (20, 21) are negligible 
with respect to the currents on the output and common leads. Thus, the sum 
of the drive currents provided by fixed current sources 15 into common 
port 18 equals the sum of the output currents on output port 19 of 
differential-transconductance amplifier 14. A variation in the modulation 
input voltage on modulation input port 11 of modulator 10 and, thus, on 
input port 17 of differential-transconductance amplifier 14 will produce a 
change in amplifier 14's differential output current on its output port 
19. 
As shown in FIGS. 1 and 2, current sensing resistor R.sub.1 is connected 
across the two leads of common port 18 of differential-transconductor 
amplifier 14 to provide local feedback in modulator 10. As shown in FIG. 
3, a single fixed current source 22 can be used with two current sensing 
resistors having a value of one-half R.sub.1 each to provide the necessary 
drive currents. 
Variable-transconductance circuitry 16 receives the carrier input signal 
V.sub.c (t) on carrier input port 12 and also receives the differential 
output current from output port 19 of differential-transconductance 
amplifier 14. The gain between carrier input and modulated output of 
variable-transconductance 16 is varied by variable-transconductance 
circuitry 16's response to the differential output current received from 
differential-transconductance amplifier 14 thus providing modulation of 
the carrier input signal. 
One specific embodiment of variable-transconductance four-quadrant 
Gilbert-type modulator 10 is shown in FIG. 4. That circuit schematic is 
taken from Motorola Semiconductors' "Specifications and Applications 
Information MC1595L/MC1495L" concerning Motorola's linear four-quadrant 
multiplier integrated circuit. The complete schematic illustrated in FIG. 
4 shows a linearized Gilbert-type multiplier; however, the right-half of 
the schematic is a common modulator of the type described above and 
illustrated in FIGS. 1 and 2. The schematic includes designations to show 
corresponding parts between the block diagramatic parts of modulator 10 in 
FIG. 1 with those parts in the schematic in FIG. 4. The schematic also 
contains the integrated circuit pin numbering P1 through P14 for the 
Motorola MC1595L chip. Furthermore, the schematic of FIG. 4 shows current 
sensing resistor R.sub.1 added which is not provided on the Motorola chip 
itself. 
The desired modulated output of the modulator is 
EQU V.sub.out (t)=A(t).times.sin.omega..sub.c t, (1) 
where the angular frequency .omega..sub.c is the carrier frequency and A(t) 
is the modulation signal. The actual input voltages to the modulator are a 
carrier input signal voltage V.sub.c (t)=V.sub.r sin.omega..sub.c t and a 
modulation input voltage V.sub.b (t)=A(t). With these input voltages, the 
ideal modulator output would be 
EQU V.sub.out =(V.sub.c .times.V.sub.b)/V.sub.m, (2) 
where 1/V.sub.m is a scale factor constant which determines the magnitude 
of the output voltage. 
In practice, however, modulators have two significant deficiencies. The 
non-ideal modulator's deficiencies are a complicated function of the 
modulator's two inputs A=A(t) and B=V.sub.r sin.omega..sub.c t and can be 
expressed using a Taylor series expansion as follows: 
##EQU1## 
In the ideal case, k.sub.11 =V.sub.r /V.sub.m and all other k.sub.ij =0. 
The more important deficiencies in the non-ideal modulator are 
non-linearity and carrier feedthrough. A non-linear relationship between 
the modulation input and the modulated output, particularly at frequencies 
near the carrier frequency, is of considerable concern. Such non-linearity 
in an AM transmitter results in distortion in the demodulated signal in 
the receiver. In an MRI system, the unwanted non-linearity would cause the 
generation of imprecise pulses of modulated RF current which, in turn, 
results in imprecise generation of the necessary alternating magnetic 
field and, therefore, the incorrectly controlled excitation of the nuclei 
of the body being studied. The end result would be an ill-defined image. 
Each of the terms after the first line in equation (3) above can be 
classified as non-linearity. In a normal case where the modulation signal 
is a much lower frequency than the carrier frequency (for example, an 
audio signal for modulation and radio frequency for the carrier), the most 
important non-linearity terms of equation (3) are those in the second line 
of the equation. Those terms give the non-linear relationship between the 
modulation input and the RF output at frequencies near the carrier 
frequency. The other significant non-linear terms will appear at 
frequencies far removed from the carrier frequency. 
Unwanted carrier feedthrough arises in a modulator where the output voltage 
Vout is not zero when the modulation input signal A(t) is zero. For 
example, in the MRI system, with carrier feedthrough the modulator cannot 
"shut off" the RF excitation of the nuclei completely. In equation (3) 
above, the k.sub.01 B term is the unwanted carrier feedthrough term. 
Typically, the contribution from this term in the modulator output voltage 
can be cancelled by shifting the zero of the modulation input signal A(t) 
slightly so that the k.sub.01 term is cancelled by the k.sub.11 term. 
There are, however, usually other mechanisms in a modulator, such as 
capacitance from the carrier input to the modulated output, which bypass 
the modulator and cannot be totally cancelled by the shifting of the zero 
of the modulation input signal. 
Another concern arising from the undesired carrier feedthrough appears when 
the modulation input is a function of time. In such a situation, when a 
sine wave having a d.c. level of zero is applied to the modulation input, 
the modulated output at the carrier frequency should be zero giving the 
desired suppressed carrier attributes of the modulator. However, in the 
prior art modulators, there is a measured output at the carrier frequency 
which is a function of the sine wave amplitude of the input even when the 
d.c. level of the input is accurately set to zero. 
Other deviations from the ideal output voltage of a modulator include the 
d.c. offset term k.sub.00 shown in equation (3), the modulation input 
feedthrough k.sub.10 term, and the terms in the third line of equation 
(3). The d.c. offset term k.sub.00 is not usually important since output 
circuitry after the modulator can contain circuitry which does not respond 
to d.c. Since the modulation input feedthrough k.sub.10 is far below the 
carrier frequency and the terms in the third line of equation (3) give 
outputs close to harmonics of the carrier frequency, all of those terms 
can be removed by a suitable bandpass filter after the modulator's output. 
Such a filter would pass only frequencies near the carrier frequency and 
would reject both low frequencies (d.c. and modulation) and specified high 
frequencies (harmonics of the carrier frequency). 
Even with the use of bandpass filters as discussed above and with the use 
of zero shifting of the modulation input signal A(t), the existing 
variable-transconductance four-quadrant Gilbert-type modulators are still 
effected by unwanted non-linearity and carrier feedthrough in their 
outputs. Thus, from the above discussion, it should be apparent that there 
is a great need for an improved balanced modulator in which the problems 
of undesired non-linearity and carrier feedthrough are alleviated. 
It is, thus, intended that the invention provide a 
variable-transconductance four-quadrant Gilbert-type modulator in which 
there is improved performance. 
Another intent is that the invention provide a balanced modulator in which 
non-linearity between the modulation input and the modulated output is 
reduced. 
Still another intent is that the invention provide a balanced modulator 
with reduced carrier feedthrough. 
Other intentions and features of the invention will further become apparent 
with reference to the accompanying drawings and the detailed description 
of the invention or may be learned by practice of the invention. 
SUMMARY OF THE INVENTION 
To achieve the foregoing intentions and in accordance with the purpose of 
the invention, as embodied and broadly described herein a 
variable-transconductance four-quadrant Gilbert-type modulator has a 
differential-transconductance amplifier, having an input port for 
receiving an input voltage signal, an output port for a differential 
output current, and a common port having two leads, for providing a change 
in its differential output current on its output port when the voltage 
signal on its input port changes and a fixed current source for providing 
drive currents to the two leads of the common port of the 
differential-transconductance amplifier, the sum of the drive currents 
being approximately equal to the sum of the output currents of the 
differential-transconductance amplifier. 
The modulator also has a current sensing resistor across the two leads of 
the common port of the differential-transconductance amplifier and has 
variable-transconductance circuitry, operatively connected to the output 
port of the differential-transconductance amplifier to receive the 
differential output current, having a carrier input port for receiving a 
carrier input signal, and having a modulated output port, responsive to 
the differential output current of the differential-transconductance 
amplifier to vary the gain of the carrier input signal to provide the 
modulated output. 
Feedback circuitry is also provided in the modulator. The circuitry has a 
modulation input port for receiving a modulation voltage signal, a 
modulation output port operatively connected to the input port of the 
differential-transconductance amplifier for providing the modulator 
voltage signal to the differential-transconductance amplifier, and a 
feedback port with two leads operatively connected across the current 
sensing resistor, for causing the voltage across the current sensing 
resistor to follow the voltage of the modulation voltage signal thereby 
causing the differential output current of the 
differential-transconductance amplifier to be directly proportional to the 
voltage signal on its input port. 
In a preferred embodiment, the feedback circuitry comprises a first 
operational amplifier having its non-inverting input operatively connected 
to one lead of the modulation input port, its inverting input operatively 
connected to one end of the current sensing resistor, and its output 
operatively connected to one lead of the input port of the 
differential-transconductance amplifier; and a second operational 
amplifier having its noninverting input operatively connected to the other 
lead of the modulation input port, its inverting input operatively 
connected to the other end of the current sensing resistor, and its output 
operatively connected to the other lead of the input port of the 
differential-transconductance amplifier. The outputs of the two 
operational amplifiers are the modulation output port of the feedback 
circuitry, the non-inverting inputs of the two operational amplifiers are 
the modulation input port of the feedback circuitry, and the inverting 
inputs of the two operational amplifiers are the feedback port of the 
feedback circuitry. 
The variable-transconductance four-quadrant Gilbert-type modulator can also 
include an output amplifier, operatively connected to the modulated output 
port, for improving isolation between the carrier input signal and the 
modulated output by reducing the impedance on the modulated output port. 
In a preferred embodiment, the output amplifier means comprises a pair of 
matched JFETs having their gates grounded, the source of one JFET 
operatively connected to one lead of the modulated output port, the source 
of the other JFET operatively connected to the other lead of the modulated 
output port, and the drains of the JFETs are the output of the output 
amplifier.

Reference will now be made in detail to the present preferred embodiments 
of the invention, examples of which are illustrated in the accompanied 
drawings. 
DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Referring again to the drawings, wherein like reference characters 
designate like or corresponding parts through the several drawings, there 
is shown in FIG. 5 variable-transconductance four-quadrant Gilbert-type 
modulator 50 in block diagrammatic form, a preferred embodiment of the 
invention. As shown in FIG. 5, improved balanced modulator 50 includes the 
basic variable-transconductance four-quadrant Gilbert-type modulator 10 
shown in FIG. 1 and discussed above with feedback circuitry 51 and output 
amplifier 52 to reduce, respectively, unwanted non-linearity and carrier 
feedthrough of modulator 10. 
As discussed above, the input on input port 17 controls the differential 
output current of amplifier 14 which is fed out of port 19 into 
variable-transconductance circuitry 16. The variation in that differential 
output current controls the gain from the carrier input to the output of 
variable-transconductance circuitry 16 to produce the modulated output. To 
improve the linearity of the differential output current of amplifier 14 
with respect to the modulation input voltage and, thus, to improve the 
linearity of the modulated output with respect to the modulation input 
voltage, feedback circuitry 51 is added to modulator 10 as shown in FIG. 
5. 
Feedback circuitry 51 includes modulation input port 53 for receiving the 
modulation input voltage signal A(t), modulation output port 54 
operatively connected to input port 17 of differential-transconductance 
amplifier 14 for providing the modulation voltage signal to amplifier 14, 
and feedback port 55 having two leads operatively connected across current 
sensing resistor R.sub.1. Feedback circuitry 51 causes the voltage across 
current sensing resistor R.sub.1 to follow the voltage of the modulation 
input voltage signal on modulation input port 53 and being fed into input 
port 17 of amplifier 14. This feedback taken from current sensing resistor 
R.sub.1 thus causes the current through resistor R.sub.1 to be directly 
proportional to the modulation input voltage which, in turn, causes the 
differential output current of amplifier 14 to be directly proportional to 
the voltage signal on its input port 17. This feedback provides a 
significant improvement in linearity of the modulated output at port 13 
with respect to the modulation input voltage signal input into modulator 
50. 
A specific embodiment of the circuitry in feedback circuitry 51 is 
illustrated in FIG. 6. As shown in FIG. 6, two operational amplifiers 60, 
61 are utilized with feedback taken from current sensing resistor R.sub.1 
(not shown in FIG. 6). Specifically, operational amplifier 60 has its 
non-inverting input 62 operatively connected to one lead of modulation 
input port 53 and its inverting input 63 operatively connected to one end 
of current sensing resistor R.sub.1. Output 64 of operational amplifier 60 
is operatively connected to one lead of input port 17 of 
differential-transconductance amplifier 14 (not shown in FIG. 6). 
Similarly, the second operational amplifier 61 has its noninverting input 
65 operatively connected to the other lead of modulation input port 53 and 
its inverting input 66 operatively connected to the other end of current 
sensing resistor R.sub.1. Output 67 of operational amplifier 61 is 
operatively connected to the other lead of input port 17 of amplifier 14. 
As shown in FIG. 6, the outputs 64, 67 of the two operational amplifiers 
60, 61 are modulation output port 54 of feedback circuitry 51. The 
non-inverting inputs 62, 65 of the two operational amplifiers are 
modulation input port 53 of feedback circuitry 51, and the inverting 
inputs 63, 66 of the two operational amplifiers are feedback port 55 of 
the feedback circuitry. 
The feedback circuitry causes the voltage on one end of current sensing 
resistor R.sub.1 to follow the voltage on one lead of the modulation input 
port and causes the voltage on the other end of R.sub.1 to follow the 
voltage on the other lead of the modulation input port. In the 
configuration shown in FIG. 6, for example, the feedback circuitry forces 
the voltage on input 63 (that is, one end of current sensing resistor 
R.sub.1) to follow the voltage on input 62 (that is, one lead of 
modulation input port 53). Similarly, the voltage on input 66 will follow 
the voltage on input 65. If desired, one lead of the modulation input port 
could be grounded, thus causing the voltage on one end of R.sub.1 to go to 
zero. With the feedback circuitry, as desired, the voltage across current 
sensing resistor R.sub.1 is forced to follow the voltage of the modulation 
input voltage signal. As would be obvious to a person of ordinary skill in 
the art upon reviewing this disclosure, additional circuitry including 
power supplies are necessary to provide the desired operation of the 
feedback circuitry. One practical circuit is detailed below with reference 
to FIG. 8. 
The above feedback circuitry produces the desired linearity improvement. To 
reduce the undesired carrier feedthrough of modulator 10, output amplifier 
52 is connected to modulator output port 13 as shown in the improved 
balanced modulator 50 of FIG. 5. Output amplifier 52 produces improved 
isolation between the carrier input signal on carrier input port 12 and 
the modulated output port 13. The output amplifier is an isolation 
amplifier which reduces the impedance seen by modulator 10 itself thereby 
increasing the carrier bandwidth of the circuitry and reducing the 
undesired capacitive coupling which exists external to the circuitry of 
modulator 10 itself. 
A preferred embodiment of output amplifier 52 is shown in FIG. 7. Amplifier 
52 has an input port 70 and output port 71 and includes a pair of matched 
JFETs 72, 73. The gates of the JFETs are grounded. The source of JFET 72 
is one lead of the isolation amplifier's input port 70 and is operatively 
connected to one lead of modulator output port 13. The drain of that JFET 
is one lead of output port 71 of amplifier 52. Similarly, the source of 
JFET 72 is the other lead of input port 70 which is operatively connected 
to the other lead of modulated output port 13, and the drain of that JFET 
is the other lead of output port 71 of output amplifier 52. The necessary 
operating voltage for the gates of the JFETs is provided at terminal 74. 
The modulated output with improved carrier suppression is outputted from 
improved balanced modulator 50 at amplifier port 71. 
A practical circuit incorporating both of the above-described improvements 
is shown in FIG. 8. The circuit utilizes the Motorola MC1595L chip 
discussed above, which chip is designated element 80 on FIG. 8. The 
feedback circuitry is shown as operational amplifier circuit 81 comprising 
operational amplifiers 60, 61 and associated components are R.sub.2 to 
R.sub.10, R.sub.27, C.sub.1 to C.sub.6, C.sub.21, and C.sub.22, along with 
current sensing resistor R.sub.1, connected to the "X" input of chip 80. 
Output amplifier circuit 82 uses dual matched JFETs 72, 73 connected 
between the "Z" outputs of chip 80 and an output transformer T2. The 
carrier input is coupled to the "Y" input of chip 80 via center-tapped 
transformer T1. 
In addition to well known components necessary to provide power to and 
control of chip 80, operational amplifiers 60, 61 and JFETs 72, 73, the 
practical circuitry in FIG. 8 includes capacitors C.sub.17 and C.sub.20 on 
output 71 of the output amplifier to assist in balancing the circuit at 
high frequencies. Capacitors C.sub.10 and C.sub.19 were added to flatten 
the frequency response of chip 80 from the carrier ("Y") input to the chip 
output ("Z"). Potentiometers R.sub.27 and R.sub.29 have been added to 
adjust for d.c. balance. R.sub.27 is useful in adjusting the carrier 
suppression so that when the modulation input is zero, the output at 
carrier frequency can be adjusted to zero. R.sub.29 is useful in adjusting 
the suppression of the modulation component in the output. Potentiometer 
R.sub.28 has been added to adjust the gain of chip 80 in the normal 
manner. 
Concerning the component values of the above briefly discussed practical 
circuitry, a person of ordinary skill in the art can readily select the 
desired component values and adjust the improved balanced modulator by 
utilizing the information provided in this disclosure, the information 
known on chip 80, and by the use of textbook circuit analysis. 
The above practical circuit provides an improved performance over the prior 
art variable-transconductance four-quadrant Gilbert-type modulators in 
both linearity and carrier suppression. 
It will be apparent to those skilled in the art that various modifications 
and variations can be made in the variable-transconductance four-quadrant 
Gilbert-type modulator of the present invention without departing from the 
scope or spirit of the invention. For example, the feedback circuitry can 
be utilized in both the "X" and "Y" inputs of a four-quadrant Gilbert-type 
multiplier to improve the linearity performance of the multiplier. 
Additionally, the input ports for modulation input and carrier input can 
be reversed. Thus, it is intended that the present invention covers the 
modifications and variations of this invention provided they come within 
the scope of the appended claims and their equivalents.