# Patent

## Title
Circuits for low noise amplifiers

## Abstract

Low noise amplifiers (LNAs) are provided, the LNAs comprising: a common gate matching network; a capacitord; a resistord; a coild, wherein a side1 of coild is coupled to a side1 of capacitord, a side1 of resistord, and a V+ and a side2 of the coild is coupled to a side2 of capacitord, a side2 of resistord, and a network input; a capacitors; a resistors; a coils, wherein a side1 of coils is coupled to an LNA input, a side1 of capacitors, a side1 of resistors, and a network output and a side2 of coils is coupled to a side2 of the capacitors, a side2 of resistors, and ground; and an output coil that is magnetically coupled to coild and coils and having a side1 coupled to a first terminal of an LNA output and a side2 coupled to a second terminal of the LNA output.

## Background
CROSS REFERENCE TO RELATED APPLICATION
This application claims the benefit of U.S. Provisional Patent Application No. 61/920,744, filed Dec. 25, 2013, which is hereby incorporated by reference herein in its entirety.


STATEMENT REGARDING GOVERNMENT FUNDED RESEARCH
This invention was made with government support under grant CCF-0964497 awarded by the National Science Foundation. The government has certain rights in the invention.


BACKGROUND
Low Noise Amplifiers (LNAs) are an integral part of many high performance receivers and their design in the literature with noise figures <3 dB has typically been limited to the use of source-degenerated LNAs and noise-cancelling LNAs. While the former provide impressive noise figure numbers using two to three integrated inductors in a CMOS technology, they suffer from degraded linearity from the passive gain in the input matching network. Noise-cancelling LNAs, on the other hand, typically achieve comparable noise figures with linearity, albeit at the cost of dramatically high power consumption spent in realizing the noise-cancelling network by active means.
FIG. 1 shows an example 100 of a typical block diagram of a noise cancelling LNA circuit using a “common-gate (CG) matching network.” As illustrated, circuit 100 may include a common gate matching network 108, a drain resistor Rd 114, a source resistor Rs 116, a first amplifier 120, a second amplifier 118, and an adder 122.
As also shown in FIG. 1, any suitable antenna/source 102 can provide an input signal to the LNA circuit, and antenna/source 102 may be represented as a voltage source 104 and an output resistance 106.
As used herein, the term “common-gate matching network” refers to the broad class of LNAs using a common gate input stage with or without gain boosting at the gate.
The noise from the CG matching network can be modeled as a current source (in) 124 as shown in FIG. 1. It can be shown that the transfer function of in has a null when the gains A1 of amplifier 120 and A2 of amplifier 118 are related as A1/A2=a(1+R0/RS)/(1−R0/RS), where a is the gain of the CG matching network and, when the LNA is matched to its input, a=Rd(1−R0/Rs)/Rs. The realization of the gains A1 and A2 is typically done by active means and hence the noise and distortion characteristics of the LNA are ultimately limited by the linearity and noise of the amplifiers, A1 and A2.
SUMMARY
Circuits for low noise amplifiers are provided. In some embodiments, low noise amplifiers (LNAs) having an LNA input and an LNA output are provided, the LNAs comprising: a common gate matching network having a network input and a network output; a drain capacitor having a first side and a second side; a drain resistor having a first side and a second side; a drain coil having a first side and a second side, wherein the first side of the drain coil is coupled to the first side of the drain capacitor, the first side of the drain resistor, and a positive supply voltage and the second side of the drain coil is coupled to the second side of the drain capacitor, the second side of the drain resistor, and the network input; a source capacitor having a first side and a second side; a source resistor having a first side and a second side; a source coil having a first side and a second side, wherein the first side of the source coil is coupled to the LNA input, the first side of the source capacitor, the first side of the source resistor, and the network output and the second side of the source coil is coupled to the second side of the source capacitor, the second side of the source resistor, and a supply voltage ground; and an output coil that is magnetically coupled to the drain coil and the source coil and having a first side coupled to a first terminal of the LNA output and a second side coupled to a second terminal of the LNA output.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 shows an example of a typical block diagram of a noise cancelling low noise amplifier circuit using a “common-gate (CG) matching network” in accordance with the prior art.
FIG. 2 shows an example of a low noise amplifier using passive voltage gain and summation in accordance with some embodiments.
FIG. 3 shows a plan view of coils that can be used in a low noise amplifier using passive voltage gain and summation in accordance with some embodiments.
FIG. 4 shows a perspective view of some coils that can be used in a low noise amplifier using passive voltage gain and summation in accordance with some embodiments.
FIG. 5 shows a perspective view of other coils that can be used in a low noise amplifier using passive voltage gain and summation in accordance with some embodiments.



DETAILED DESCRIPTION
FIG. 2 shows an example 200 of a low noise amplifier (LNA) circuit using passive voltage gain and summation in accordance with some embodiments. As shown, circuit 200 includes a common-gate (CG) matching network 108, a drain capacitor 202, a drain resistor 204, a drain coil 206, a source capacitor 208, a source resistor 210, a source coil 212, and an output coil 214.
As also shown in FIG. 2, any suitable antenna/source 102 can provide an input signal to the LNA circuit, and antenna/source 102 may be represented as a voltage source 104 and an output resistance 106.
As further shown in FIG. 2, the output of LNA circuit 200 can be represented by Vout, which is provided at a load connected to output coil 214. This load can be represented by load capacitors 216 and 218 and can provide a high impedance load on the coil.
Common-gate (CG) matching network 108 as shown in circuit 200 can be any suitable CG matching network and can have any suitable components.
Drain capacitor 202, drain resistor 204, source capacitor 208, and source resistor 210 can be any suitable capacitors and resistors, and these components can have any suitable values.
Coils 206, 212, and 214 can be magnetically coupled to form a transformer. This transformer can passively provide the voltage gain and summation of active amplifiers without adding the corresponding noise. Any suitable coils can be used in some embodiments. For example, in some embodiments, coils 206 and 214 form a transformer with turns ratio n2:n1 and coils 212 and 214 form a transformer with turns ratio 1:n1.
In some embodiments, by labeling coils 212, 206, and 214 as Ls, Ld, and Lout, respectively, the overall gain desired from the LNA as G, and the center frequency of the LNA as f, the following equations can be used to determine values for the corresponding components:

Lout=n12Ls 

Ld=n22Ls 

n2=Rd(1+R0/Rs)/Rs 

Cd=−0.5(n12/n22)Cload+1/(4π2f2Ld)

Cs=−0.5n12Cload+1/(4π2f2Ls)

n1=G/2

FIG. 3 shows a plan, layout view of three magnetically coupled coils that can be used with the circuit of FIG. 2 in accordance with some embodiments. As shown, the coils of FIG. 3 can connect to the circuit of FIG. 2 via the terminals identified in each as A+, A−, B+, B−, C+, and C−. As also shown, the coils can be formed from five loops 302, 304, 306, 308, and 310. That is coil 206 can be formed by loops 306 and 308 and connection 314, coil 212 can be formed by loops 302 and 310 and connection 312, and coil 214 can be formed by loop 304.
FIG. 4 shows a perspective view of an example of loops 304, 306, and 308 in accordance with some embodiments. As illustrated, these loops can be formed in a semi-conductor wafer in three metalization layers. More particularly, for example, a partial loop 402 can be formed in an upper metalization layer, a partial loop 404 can be formed in a middle metalization layer, and a partial loop 406 can be formed in a lower metalization layer. These partial loops can be connected together by links 408 and 410 to form a coil. The coil can be connected to other components via connections 412 and 414.
FIG. 5 shows a perspective view of an example of loops 302 and 310 in accordance with some embodiments. As illustrated, these loops can be formed in a semi-conductor wafer in three metalization layers. More particularly, for example, a partial loop 502 can be formed in an upper metalization layer, a partial loop 504 can be formed in a middle metalization layer, and a partial loop 506 can be formed in a lower metalization layer. These partial loops can be connected together by vias 508 to form a coil. Any suitable number of vias 508 can be provide between the partial loops. For example, eight vias can be provided in some embodiments, and these vias may be equally spaced along the length of the partial loops. The coil can be connected to other components via connections 510 and 512.
Although the examples provided herein use transformers to provide a passive gain, any suitable components can be used to provide passive gains in some embodiments. For example, other uses of coils and capacitors can be used in some embodiments.
Although the invention has been described and illustrated in the foregoing illustrative embodiments, it is understood that the present disclosure has been made only by way of example, and that numerous changes in the details of implementation of the invention can be made without departing from the spirit and scope of the invention, which is limited only by the claims that follow. Features of the disclosed embodiments can be combined and rearranged in various ways.

## Claims

1. A low noise amplifier (LNA) having an LNA input and an LNA output, comprising:
a common gate matching network having a network input and a network output;
a drain capacitor having a first side and a second side;
a drain resistor having a first side and a second side;
a drain coil having a first side and a second side, wherein the first side of the drain coil is coupled to the first side of the drain capacitor, the first side of the drain resistor, and a positive supply voltage and the second side of the drain coil is coupled to the second side of the drain capacitor, the second side of the drain resistor, and the network input;
a source capacitor having a first side and a second side;
a source resistor having a first side and a second side;
a source coil having a first side and a second side, wherein the first side of the source coil is coupled to the LNA input, the first side of the source capacitor, the first side of the source resistor, and the network output and the second side of the source coil is coupled to the second side of the source capacitor, the second side of the source resistor, and a supply voltage ground; and
an output coil that is magnetically coupled to the drain coil and the source coil and having a first side coupled to a first terminal of the LNA output and a second side coupled to a second terminal of the LNA output.

2. The LNA of claim 1, wherein the source coil and the output coil form a transformer with turns ratio 1:n1 and the drain coil and the output coil form a transformer with turns ratio n2:n1.

3. The LNA of claim 1, wherein the drain coil is formed from two coils connected in series.

4. The LNA of claim 3, wherein each of the two coils is formed over at least three layers of a semiconductor wafer using a partial loop in each of the at least three layers and a connection between each adjacent pair of the at least three layers that connects which connects the each partial loop in series.

5. The LNA of claim 4, wherein each of the partial loops is square.

6. The LNA of claim 1, wherein the output coil is formed over at least three layers of a semiconductor wafer using a partial loop in each of the at least three layers and a connection between each adjacent pair of the at least three layers that connects which connects the each partial loop in series.

7. The LNA of claim 6, wherein each partial loop is rectangular.

8. The LNA of claim 1, wherein the source coil is formed from two partial loops connected in series.

9. The LNA of claim 8, wherein each of the two partial loops is formed over at least three layers of a semiconductor wafer using a partial loop in each of the at least three layers and a plurality of connections between each adjacent pair of the at least three layers that connects which connects the each partial loop in parallel.

10. The LNA of claim 8, wherein one of the two partial loops is rectangular.

11. The LNA of claim 8, wherein one of the two partial loops is square.

12. The LNA of claim 1, wherein the common gate matching network comprises:
an operational amplifier with a first input coupled to a reference voltage, a second input, and an output; and
a field effect transistor having a gate connected to the output of the operation amplifier, an drain connected to the network input, and a source connected to the network output and the second input of the operational amplifier.