The Actively Loaded MOSFET Differential Pair: Output Resistance

In this article, we’ll discuss MOSFET small-signal output resistance as we make our way toward predicting the gain of the actively loaded differential pair.

The Effect of Channel-Length Modulation

In the two previous articles, we introduced the actively loaded MOSFET differential pair and discussed two prominent advantages of this configuration—namely, improved biasing (compared to the use of drain resistors) and differential-to-single-ended conversion without loss of gain.
Now it’s time to analyze the differential gain of this circuit; before we can determine the gain, though, we need to understand the concept of small-signal output resistance and how we incorporate this resistance into our analysis. (If you’re not sure what I mean by “small-signal,” take a look at the “Two Outputs or One?” section in this article.)
The first thing to understand is that small-signal output resistance is not an inherent, precise property of a real MOSFET. Rather, it is a model that we use to account for the effect of channel-length modulation on a MOSFET’s small-signal behavior. Recall that MOSFETs used for linear amplification are typically biased in the saturation region, which corresponds to when the FET’s channel is “pinched off” at the drain end.



In a simplified analysis, we use the following equation for saturation-mode drain current:



This equation conveys the assumption that drain current is not affected by the drain-to-source voltage. The MOSFET acts like a dependent current source controlled by the overdrive voltage VOV, where VOV = VGS – VTH. This assumption is based on the idea that increasing the drain-to-source voltage does not alter the channel once it has become pinched off.
As you’ve probably noticed, though, the real world is not particularly conducive to idealized situations such as this.
The reality is that increasing the drain-to-source voltage does have a nontrivial effect on the channel: the pinch-off point is moved toward the source, and the result is more drain-to-source current as drain-to-source voltage increases. This means that we need an additional circuit element to account for this additional current, and by now you have probably guessed that the element we’re looking for is a resistor—namely, the small-signal output resistance ro.



So now we have a MOSFET, which is still assumed to be immune to increasing drain-to-source voltage, in conjunction with an ordinary resistor, which (like any resistor) has a current flow equal to the voltage across the resistor divided by the resistance. As drain-to-source voltage increases, more current flows through the resistor, and this current compensates for the lack of change in the drain current of the idealized MOSFET. By combining these two currents—drain current of the idealized FET and current through the resistor—we can find the total drain current for a real MOSFET.
Ignoring channel-length modulation is equivalent to assuming that the small-signal output resistance of the FET is infinite. It follows, then, that higher output resistance is desirable if we want a MOSFET to behave more like the idealized component in which drain current is not influenced by drain-to-source voltage. As we will see later, small-signal output resistance is determined in part by the FET’s DC bias current, so we do have some ability to increase the output resistance of a given device.
One last note before we move on: Output resistance is itself a simplification of real MOSFET behavior. The subatomic action taking place in a MOSFET’s channel is not exactly straightforward, and it comes as no surprise to me that the simple linear relationship represented by a drain-to-source resistor is not the whole story.

Reducing Gain

How does finite small-signal output resistance affect the performance of a MOSFET amplifier? Consider the following circuit:



This is a basic common-source amplifier. We’re concerned only with small-signal behavior here, which means that 1) the biasing circuitry is omitted and 2) you can assume that the FET is in saturation. As discussed in the first section of The MOSFET Differential Pair with Active Load, the magnitude of this amplifier’s gain is the MOSFET’s transconductance multiplied by the drain resistance:



Now let’s incorporate the finite output resistance:



And next we recall that the small-signal analysis technique allows us to replace constant DC voltage sources with short circuits. The result is the following:



Now the effect of the output resistance is clear—it is in parallel with the drain resistor, and thus the magnitude of the voltage gain becomes the following:



So the finite output resistance lowers the gain, because the equivalent resistance of two resistors in parallel is always less than that of either individual resistor. This demonstrates the desirability of higher small-signal output resistance: if ro is much larger than RD, the reduction in gain will be negligible. Notice also that the output resistance places an upper limit on AV; no matter how much drain resistance you have, the equivalent resistance RD||ro will never be higher than ro. This means that AV cannot exceed (gm × ro), which is referred to as a MOSFET’s intrinsic gain.

Lambda

OK, so how do we calculate the small-signal output resistance? You need two things: bias current and lamba (or λ, for those who are a little foggy on the Greek alphabet).



Lambda depends on physical characteristics of the FET and on the device’s bias conditions, but to make life tolerably simple we ignore the dependence on bias conditions and assume that lambda is a constant for a particular process technology.
You should be aware, though, that lambda increases as the length of the physical channel decreases. ID (fortunately more straightforward than lambda) is the FET’s DC-bias drain current—i.e., the drain current that you ignore when performing small-signal analysis.
I looked through some NMOS SPICE models and saw lambda values in the range of, say, 0.01 to 0.1 V–1. With a bias current of 500 µA, this range corresponds to small-signal output resistance of 200 kΩ to 20 kΩ.
This gives you an idea of the high gains we can achieve by loading an amplifier with a transistor’s small-signal output resistance instead of an ordinary drain resistor (if you find this statement confusing, refer back to “The Drain-Resistor Problem” and “Thinking About a Current Source” in this article). Keep in mind, though, that state-of-the-art short-channel MOSFETs will have higher lambda (and thus lower gain).

Conclusion


Now that we have explored small-signal output resistance, we are ready to analyze the differential gain of our actively loaded MOSFET differential pair. We’ll do this in the next article, and we’ll also empirically (i.e., via simulation) measure lambda so that we can predict the gain of an LTspice differential amplifier.
Previous
Next Post »
My photo

Hi, I`m Sostenes, Electrical Technician and PLC`S Programmer.
Everyday I`m exploring the world of Electrical to find better solution for Automation. I believe everyday can become a Electrician with the right learning materials.
My goal with BLOG is to help you learn Electrical.
Related Posts Plugin for WordPress, Blogger...

Label

KITAIFA NEWS KIMATAIFA MICHEZO BURUDANI SIASA TECHNICAL ARTICLES f HAPA KAZI TU. LEKULE TV EDITORIALS ARTICLES DC DIGITAL ROBOTICS SEMICONDUCTORS MAKALA GENERATOR GALLERY AC EXPERIMENTS MANUFACTURING-ENGINEERING MAGAZETI REFERENCE IOT FUNDAMENTAL OF ELECTRICITY ELECTRONICS ELECTRICAL ENGINEER MEASUREMENT VIDEO ZANZIBAR YETU TRANSDUCER & SENSOR MITINDO ARDUINO RENEWABLE ENERGY AUTOMOBILE SYNCHRONOUS GENERATOR ELECTRICAL DISTRIBUTION CABLES DIGITAL ELECTRONICS AUTOMOTIVE PROTECTION SOLAR TEARDOWN DIODE AND CIRCUITS BASIC ELECTRICAL ELECTRONICS MOTOR SWITCHES CIRCUIT BREAKERS MICROCONTROLLER CIRCUITS THEORY PANEL BUILDING ELECTRONICS DEVICES MIRACLES SWITCHGEAR ANALOG MOBILE DEVICES CAMERA TECHNOLOGY GENERATION WEARABLES BATTERIES COMMUNICATION FREE CIRCUITS INDUSTRIAL AUTOMATION SPECIAL MACHINES ELECTRICAL SAFETY ENERGY EFFIDIENCY-BUILDING DRONE NUCLEAR ENERGY CONTROL SYSTEM FILTER`S SMATRPHONE BIOGAS POWER TANZIA BELT CONVEYOR MATERIAL HANDLING RELAY ELECTRICAL INSTRUMENTS PLC`S TRANSFORMER AC CIRCUITS CIRCUIT SCHEMATIC SYMBOLS DDISCRETE SEMICONDUCTOR CIRCUITS WIND POWER C.B DEVICES DC CIRCUITS DIODES AND RECTIFIERS FUSE SPECIAL TRANSFORMER THERMAL POWER PLANT cartoon CELL CHEMISTRY EARTHING SYSTEM ELECTRIC LAMP ENERGY SOURCE FUNDAMENTAL OF ELECTRICITY 2 BIPOLAR JUNCTION TRANSISTOR 555 TIMER CIRCUITS AUTOCAD C PROGRAMMING HYDRO POWER LOGIC GATES OPERATIONAL AMPLIFIER`S SOLID-STATE DEVICE THEORRY DEFECE & MILITARY FLUORESCENT LAMP HOME AUTOMATION INDUSTRIAL ROBOTICS ANDROID COMPUTER ELECTRICAL DRIVES GROUNDING SYSTEM BLUETOOTH CALCULUS REFERENCE DC METERING CIRCUITS DC NETWORK ANALYSIS ELECTRICAL SAFETY TIPS ELECTRICIAN SCHOOL ELECTRON TUBES FUNDAMENTAL OF ELECTRICITY 1 INDUCTION MACHINES INSULATIONS ALGEBRA REFERENCE HMI[Human Interface Machines] INDUCTION MOTOR KARNAUGH MAPPING USEUL EQUIATIONS AND CONVERSION FACTOR ANALOG INTEGRATED CIRCUITS BASIC CONCEPTS AND TEST EQUIPMENTS DIGITAL COMMUNICATION DIGITAL-ANALOG CONVERSION ELECTRICAL SOFTWARE GAS TURBINE ILLUMINATION OHM`S LAW POWER ELECTRONICS THYRISTOR USB AUDIO BOOLEAN ALGEBRA DIGITAL INTEGRATED CIRCUITS FUNDAMENTAL OF ELECTRICITY 3 PHYSICS OF CONDUCTORS AND INSULATORS SPECIAL MOTOR STEAM POWER PLANTS TESTING TRANSMISION LINE C-BISCUIT CAPACITORS COMBINATION LOGIC FUNCTION COMPLEX NUMBERS ELECTRICAL LAWS HMI[HUMANI INTERFACE MACHINES INVERTER LADDER DIAGRAM MULTIVIBRATORS RC AND L/R TIME CONSTANTS SCADA SERIES AND PARALLEL CIRCUITS USING THE SPICE CIRCUIT SIMULATION PROGRAM AMPLIFIERS AND ACTIVE DEVICES BASIC CONCEPTS OF ELECTRICITY CONDUCTOR AND INSULATORS TABLES CONDUITS FITTING AND SUPPORTS CONTROL MOTION ELECTRICAL INSTRUMENTATION SIGNALS ELECTRICAL TOOLS INDUCTORS LiDAR MAGNETISM AND ELECTROMAGNETISM PLYPHASE AC CIRCUITS RECLOSER SAFE LIVING WITH GAS AND LPG SAFETY CLOTHING STEPPER MOTOR SYNCHRONOUS MOTOR AC METRING CIRCUITS APPS & SOFTWARE BASIC AC THEORY BECOME AN ELECTRICIAN BINARY ARITHMETIC BUSHING DIGITAL STORAGE MEMROY ELECTRICIAN JOBS HEAT ENGINES HOME THEATER INPECTIONS LIGHT SABER MOSFET NUMERATION SYSTEM POWER FACTORS REACTANCE AND IMPEDANCE INDUCTIVE RESONANCE SCIENTIFIC NOTATION AND METRIC PREFIXES SULFURIC ACID TROUBLESHOOTING TROUBLESHOOTING-THEORY & PRACTICE 12C BUS APPLE BATTERIES AND POWER SYSTEMS ELECTROMECHANICAL RELAYS ENERGY EFFICIENCY-LIGHT INDUSTRIAL SAFETY EQUIPMENTS MEGGER MXED-FREQUENCY AC SIGNALS PRINCIPLE OF DIGITAL COMPUTING QUESTIONS REACTANCE AND IMPEDANCE-CAPATIVE RECTIFIER AND CONVERTERS SEQUENTIAL CIRCUITS SERRIES-PARALLEL COMBINATION CIRCUITS SHIFT REGISTERS BUILDING SERVICES COMPRESSOR CRANES DC MOTOR DRIVES DIVIDER CIRCUIT AND KIRCHHOFF`S LAW ELECTRICAL DISTRIBUTION EQUIPMENTS 1 ELECTRICAL DISTRIBUTION EQUIPMENTS B ELECTRICAL TOOL KIT ELECTRICIAN JOB DESCRIPTION LAPTOP THERMOCOUPLE TRIGONOMENTRY REFERENCE UART WIRELESS BIOMASS CONTACTOR ELECTRIC ILLUMINATION ELECTRICAL SAFETY TRAINING FILTER DESIGN HARDWARE INDUSTRIAL DRIVES JUNCTION FIELD-EFFECT TRANSISTORS NASA NUCLEAR POWER SCIENCE VALVE WWE oscilloscope 3D TECHNOLOGIES COLOR CODES ELECTRIC TRACTION FEATURED FLEXIBLE ELECTRONICS FLUKE GEARMOTORS INTRODUCTION LASSER MATERIAL PID PUMP SEAL ELECTRICIAN CAREER ELECTRICITY SUPPLY AND DISTRIBUTION MUSIC NEUTRAL PERIODIC TABLES OF THE ELEMENTS POLYPHASE AC CIRCUITS PROJECTS REATORS SATELLITE STAR DELTA VIBRATION WATERPROOF