Electronics Tutorial #4: Ohms Law

If you want to build your own electronic circuits, one law you must learn and know how to use is Ohms law. Ohms law lets you calculate the current and voltage through and across a resistor. The basic equation that Ohms law states is that voltage is equal to the product of current and resistance. In equation form:

Equation 1: V= IR

If you know the voltage across a resistor and the current through a resistor you can compute the value of the resistor. Similarly, if you know the resistor value and the current through the resistor you can compute the voltage across the resistor.  For example if you put 2 Volts across a 1 Ohm resistor, from Ohms law you calculate that the current is 1 Ampere.

If you don't want to do the hand calculations required for Ohms law, you can always use a circuit simulator. The LTSpice circuit simulator, is a free simulator, that you can use to calculate the voltage across and the current through a resistor. In the LTSpice circuit schematic below, a 10 Volt battery is placed across a 1000 Ohm resistor. Using Ohms law, you can calculate that the current through the resistors would be 0.01 Ampere or 10 mA. A mA (milliamp) is 1/1000th of an Ampere.

LTSPICE Ohms Law Circuit Simulation

There are many advantages of using the LTSpice circuit simulator to analyze a circuit. One advantage is that it eliminates calculation errors. The second advantage is that you can analyze complex circuits, that would take hours of hand calculations, in seconds.  The third advantage is that it facilitates learning and allows you to build intuition about circuit design.

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Learning Links

LTSPICE Download

Electronics Tutorial #3, JFET Common Source Amplifiers

If you are a do-it-yourself electronic hobbyists or an audio enthusiast, one of the first types of circuits you want to add to your circuit collection is an amplifier. Amplifiers can be found in all sorts of electronic equipment and devices. Headphones, mixers, cell phones, PCs, stereos and radios are just a few audio applications. Medical devices, such as hearing aids and biomedical instrumentation, such as radiation sensors, also employ amplifiers. But the applications of amplifiers doesn't stop there. Robots are another area where amplifiers and sensors work together to bring new forms of artificial life.

High-quality amplifiers can be built relatively easily and inexpensively using JFET transistors. JFET transistors have low-noise and low-power characteristics that make them well-suited for high-end audio and scientific applications.

One of the most common types of JFET amplifiers is the common source amplifier. It is used to amplify a low voltage audio signal, such as which comes from a microphone. Once amplified, the signal can be into a speaker, such as those found in cell phones and tablets. 

JFET Common Source Amplifier Design

The basic design of a JFET common source amplifier is shown below. In this design, a 1 Volt peak to peak sine wave is fed into the circuit. The amplifier increases the voltage level to 5 V peak to peak. The voltage gain of the circuit is controlled with the resistors in the circuit.  In this case, since the drain resistor, Rd, is 4000 Ohms, and the source resistor, Rs, is 400 Ohms, the gain is 5 By increasing the ratio of Rd to Rs you can increase the voltage gain. Similarly, reducing the ratio reduces the gain.

                        Common Source Amplifier: LTSpice Schematic

                           

LTSpice Simulation Voltage Gain of Common Source Amplifier

Designing the Amplifier: Bias Point Considerations

The design of a common source amplifier requires that you first determine the DC  bias point. This can be determined with an LTSpice simulation. The figure below shows the results of applying a 0 V signal to the input and the resulting output  bias voltages and currents. As can be seen the DC output voltage determines the base line for the output waveform, In this case, its 10.7 volts. This can be calculated using a variety of different methods. However, often its just easier to determine it from an LTSpice simulation.

LTSpice DC Bias Point Simulation

The DC output voltage can be changed if you want. You could change  the values of the Rd and Rs resistors, but this will alter the gain of the circuit. Alternately, you could bias the gate with a DC voltage through a resistor or using a voltage divider.

Voltage Gain

The voltage gain of the circuit can be calculated from the voltage gain equation for a common source amplifier:

Equation 1: Av = -gm *Rd)/(1 + gm*Rs)

The equation requires that you know the transductance, gm,  of the transistor. The transconductance however is also a function of the bias point, specifically Vgsq. The transconductance can also be estimated from the data sheet of the manufacturer. Using an approximate estimate of the transconductance will give you a good idea of the gain. For this example, the transconductance of the LSK489 is estimated at 2.5 mA/V.  Substituting this value into the equation along with the values of the Rd and Rs gives a voltage gain of  -5.

In order for equation 1 to be valid, the value of Rd must be at least 10 times smaller than the drain resistance of the actual JFET. From the IV curves of the LSK489, the value of rd around the bias point is in the order of 50k.

All in all though, it is often easier to determine the gain very roughly with an estimated constant. For example, Av = 1/2(Rd/Rs) gives a good approximation.


Building the Circuit

If you want to breadboard the circuit, you can use a variety of different JFETs. For this example the LKS489, JFET N-Channel transistor from Linear Integrated Systems was used. This JFET has a pinchoff voltage that ranges between -1.5 and -3.5 Volts. The drain to source saturation current for the LSK489 ranges from 2.5 to 15 mA.  The transconductance ranges from around 1 millisiemens upward to 8 millisiemens (ma/V).

If you substitute different JFETs into your breadboard, you will find that the bias point and the gain will vary. This is a direct result of the fact that different JFETs have different pinchoff voltages, IDSS and transconductance specifications.

When building the actual circuit with the LSK489 you will also find that the gain and bias point  may not be what the simulator predicts. This is because JFET specifications vary from device to device and from run to run. However they always fall in between the minimum and maximum limits.

To overcome this problem, amplifier manufacturers go to great lengths to test each JFET for tighter specification limits. There are also a number of design techniques that can be used to eliminate variations in gain as a result of variations in JFET specifications.

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Learning Links 

Junction Field Effect TransistorTheory and Applications
LSK489 Data Sheet

Electronics Tutorial: JFET Current Voltage Characteristics: IV Curves with LTSpice

LTSpice offers one way to generate IV curves without an expensive curve tracer. However, how well LTSpice IV curves match the actual device’s IV curves depends on how accurately the JFET model matches the actual device. Not all LTSpice models are created equal. Some models are bare bones and will only give you a a rough estimate of the actual IV curves.  Most models include the pinchoff voltage and beta parameter, which take into account the drain to source saturation current. Additionally, most models are only specified for a given set of process conditions. This process condition most often corresponds to the minimum data specifications on the data sheet.

JFET  IV Characteristics (Curve Tracing)

The basic circuit for generating IV curves for a N channel is shown below. It utilizes two supplies,  one for generating the gate to source voltage (VGS) and one for generating the drain to source voltage (VDS). During the simulation, the gate to source voltage is kept constant and the drain to source voltage is stepped from 0 Volts to a maximum drain to source voltage. 

However, a complete set of IV curves requires that the drain-to-source current be measured at different VGS voltages.  The typical LTSpice simulation command for generating  a set of  JFET IV  curves is

.DC VDS 0  15 0.01 VGS -1.5 0 -0.3

LTSPICE Circuit Schematic for Generating IV Curves for a JFET

Th e DC sweep command instructs the simulator to first set the gate voltage to -1.5 volts and then sweep the VDS power supply from 0 to 15 volts in 0.01 volt steps. Once that sweep is complete, the VGS supply is incremented by -0.5 Volts to  -1.5 Volts and VDS is swept again from 0 to 15 volts  This process continues until VGS reaches 0 V. A N-Channel JFET is fully on when the gate-to-source voltage is 0 V. When VGS is at the pinchoff voltage the drain to source current is zero. For the default JFET LTSPICE model used in this example, the pinchoff parameter is at its default value of - 2 Volts.

IV Characteristics of Default N-Channel JFET LTSPICE Model

The default N-Channel default model also uses LAMBA = 0.  Because LAMBDA is zero, the slope of the IV curves in the saturation region is zero also.  For the most part, this is not the way a real JFET operates. The IV curves in the saturation region have a small slope, which is set with the value of LAMBDA. 

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LEARNING LINKS 

JFET SPICE DEFAULTS: http://ltwiki.org/index.php5?title=J_JFET_transistor

LTSPICE TUTORIAL  http://www.simonbramble.co.uk/lt_spice/ltspice_lt_spice_tutorial_6.htm