DIRECT CURRENT

A direct current (dc) flows in one direction , either steadily or in pulses.:

Current (I)    - The quantity of electrons passing a given point (unit : ampere)

Voltage (V) - Electrical pressure or force (unit : volt)

Resistance(R) - Resistance to the flow of a current, (unit : ohm)

Power (P) - the work performed by a current , (unit : watt)

Potential Difference - the difference in voltage between the two ends of a conductor through which a current flows , also known as a voltage drop.

OHM'S LAW

Ohm's Law Helper Diagram 

A potential difference of 1 volt will force a current of 1 Ampere through a resistance of 1 ohm, or :

V = I x R

I  = V/R

R = V/I

P = I x V (or) I^2 x R

Resistor Networks

Resistor Networks: Complete Guide, Types, Calculations, and Applications

Resistor Networks are one of the most important and widely used building blocks in electronics. They appear in almost every electronic circuit, from simple voltage dividers to advanced digital-to-analog converters, microcontroller interfaces, radio frequency systems, and industrial control equipment.

A resistor network is not just a random collection of resistors. It is a carefully designed arrangement that allows engineers to control voltage, current, signal levels, impedance, and biasing with high precision. Understanding resistor networks is essential for students, hobbyists, technicians, and professional engineers.

In this comprehensive guide, we will explore what resistor networks are, how they work, the different types of resistor networks, their formulas, design considerations, real-world applications, and common mistakes to avoid.

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What Are Resistor Networks?

Resistor networks are combinations of two or more resistors connected together in a specific configuration to achieve a desired electrical function. These resistors may be connected in series, parallel, or a mixture of both.

Instead of using individual resistors, engineers often use resistor networks to:

• Divide voltage accurately
• Control current flow
• Create reference voltages
• Set bias points for transistors and amplifiers
• Match impedances in signal paths

Resistor networks can be built using discrete resistors or manufactured as integrated resistor network packages (SIP, DIP, or surface-mount arrays).

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Why Resistor Networks Are Important in Electronics

Resistor networks simplify circuit design and improve reliability. Instead of calculating and placing many individual resistors, a properly designed resistor network ensures consistent performance, better tolerance matching, and reduced circuit complexity.

Key benefits of resistor networks include:

• Improved accuracy due to matched resistors
• Reduced PCB space
• Lower assembly cost
• Better thermal stability
• Cleaner and more organized circuit layouts

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Basic Types of Resistor Networks

Resistor Network Schematics

Series Resistor Network

Parallel Resistor Network

Interactive Resistor Network Calculator

Calculate equivalent resistance for series or parallel resistor networks.

Resistor Values (Ohms, comma separated):


Connection Type:
Series Parallel

Result:

1. Series Resistor Networks

In a series resistor network, resistors are connected end-to-end so that the same current flows through each resistor.

Total resistance:

R_total = R₁ + R₂ + R₃ + ...

Series resistor networks are commonly used in:

• Voltage divider circuits
• Current limiting
• High-voltage measurement systems

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2. Parallel Resistor Networks

In a parallel resistor network, all resistors share the same voltage, but current divides among them.

Total resistance:

1 / R_total = 1 / R₁ + 1 / R₂ + 1 / R₃ + ...

Parallel resistor networks are useful when:

• Lower resistance is required
• Current sharing is needed
• Power dissipation must be distributed

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3. Series-Parallel Resistor Networks

Most real-world resistor networks are combinations of series and parallel connections. These networks allow designers to achieve precise resistance values that may not be available with standard resistor values.

Series-parallel resistor networks are common in:

• Analog signal conditioning
• Sensor interfaces
• Instrumentation circuits

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Voltage Divider as a Resistor Network

One of the most common examples of resistor networks is the voltage divider. It consists of two or more resistors in series that divide an input voltage into smaller output voltages.

Voltage divider formula:

V_out = V_in × (R₂ / (R₁ + R₂))

Voltage divider resistor networks are widely used in:

• Microcontroller ADC inputs
• Battery voltage monitoring
• Reference voltage generation

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Ladder Resistor Networks

A ladder resistor network consists of repeating series and parallel resistor sections arranged in a ladder-like structure.

These resistor networks are used in:

• Digital-to-analog converters (DACs)
• Precision voltage scaling
• Audio attenuation circuits

Ladder resistor networks offer predictable voltage steps and excellent linearity when designed correctly.

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R-2R Resistor Networks

The R-2R resistor network is one of the most famous resistor network configurations. It uses only two resistor values: R and 2R.

Despite its simplicity, the R-2R resistor network provides high accuracy and scalability, making it ideal for DAC applications.

Advantages of R-2R resistor networks:

• Only two resistor values required
• Excellent matching accuracy
• Easy integration into ICs

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Integrated Resistor Network Packages

Modern electronics often use integrated resistor networks packaged in:

• SIP (Single Inline Package)
• DIP (Dual Inline Package)
• SMD resistor arrays

These packages contain multiple resistors with matched tolerances, improving performance in precision applications.

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Applications of Resistor Networks

1. Microcontrollers and Embedded Systems

Resistor networks are used for pull-up and pull-down resistors, voltage dividers, and analog input conditioning.

2. Audio and Signal Processing

Audio mixers, attenuators, and filters rely heavily on resistor networks for signal shaping.

3. Power Electronics

In power supplies, resistor networks provide feedback sensing, voltage scaling, and protection functions.

4. RF and Communication Systems

Resistor networks are used in impedance matching, biasing RF amplifiers, and signal sampling.

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Design Considerations for Resistor Networks

• Resistor tolerance and matching
• Power dissipation
• Thermal stability
• Noise performance
• Load interaction

Ignoring these factors can lead to inaccurate measurements, unstable circuits, or component failure.

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Common Mistakes When Using Resistor Networks

• Using resistor networks as power supplies
• Ignoring load effects
• Using mismatched resistor tolerances
• Overlooking power ratings

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Resistor Networks vs Individual Resistors

Feature	Resistor Network	Individual Resistors
Accuracy	High (matched)	Moderate
PCB Space	Compact	Larger
Cost	Lower for multiple resistors	Higher assembly cost

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Future Trends in Resistor Networks

As electronics continue to miniaturize, resistor networks are becoming more integrated into ICs and system-on-chip designs. Advanced thin-film and laser-trimmed resistor networks are pushing accuracy and stability to new levels.

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Conclusion

Resistor Networks are essential components in modern electronics. From simple voltage dividers to precision DACs and RF circuits, resistor networks provide reliable, scalable, and accurate solutions for controlling voltage and current.

By understanding resistor network types, calculations, and applications, you can design better, safer, and more efficient circuits. Whether you are a beginner or an experienced engineer, mastering resistor networks is a fundamental skill in electronics.

Recommended Resistor Network Components

Precision Resistor Network Arrays

For accurate resistor networks, matched resistor arrays provide better stability and tolerance than individual resistors.

• Vishay Precision Thin Film Resistor Network – Ideal for voltage dividers and DAC circuits
• Bourns SIP Resistor Network Pack – Perfect for microcontroller pull-up networks

Discrete Resistor Kits

• 1% Metal Film Resistor Kit (E12/E24) – Best for building custom resistor networks

An Active antenna for 160 to 4 meters

This active antenna has been doing its job in my loft for well over 10 years. l’'ve seen anumber of designs over the years, and this is the simplest, deriving from experiment. When | recently saw a highly sophisticated-looking commercial unit, | felt it was time to ‘go public’.
Active antennas rely on a combination of an antenna element (Such as a dipole, monopole, orloop) and anamplifier, which is the ‘active’ part. The antennaelementis non-resonant, and tends to be physically small. They have broad operating bandwidths, so don’t need to be tuned. In comparison, a resonant antenna would need tuner adjustments to cover the whole HF and lower VHF spectrum. So, the attraction of active antennas is convenience.
It is only fair to point out that some people dislike them, and there are pitfalls, which | shall point out. If you want a really excellent receiving antenna for all the HF amateur and broadcast bands, and have masses of space, why not put up a Beverage or rhombic antenna? If, as in my case, that’s out of the question, then consider an active antenna and, better still, try building your own! This one can be put together in a few hours and covers 160 to 4 metres.

DESIGN CONSIDERATIONS

THE CHOICE of a small antenna element (less than a tenth of a wavelength or so) is between the dipole and monopole, which respond to the electric field component of the radio wave; and the loop, which responds to the magnetic field component. A broadband active loop antenna is still on my list of things to try.
My first homebrew active antenna was a dipole, and was quite successful. The main thing it taught me was thatit’s nota good idea to have too much gain. It is natural to conclude that, as a short antenna picks up a smaller signal than a resonant dipole, the gain must be made up in the amplifier. Being a broadband device, the amplifier is subjected to the entire HF radio spectrum including powerful broadcast transmitters. What tends to happen in practice is that it distorts, generating intermodulation products. These appear to the receiver as additional signals and, though giving the impression of a ‘lively’ receiving system, are entirely unwanted. An attenuator between the active antenna and receiver is of no use at all, if the distortion has already happened in the active antenna.
It occurred to me to try asingle wire monopole, which made for a simpler amplifier. This worked and has been in use ever since.

CIRCUIT DESCRIPTION

THE AMPLIFIER, shown in Fig 1, is a source-follower circuit designed around Tr1, aJ310 FET (field-effect transistor). This has to present a high impedance to the small monopole, otherwise signal voltage is lost, and then deliver the signal to the receiver input, commonly a 50 Ohm impedance.

The FET has an output impedance in the region of 50 to 100 Ohm , which means that, if the FET source fed the receiver 50 Ohm input, more than half the signal voltage would appear across the FET, and less than half would be delivered to the receiver. That's where the transformer T1, in the source circuit, comes in. I used a quadrifilarwinding to give a 4:1 voltage step down ratio. This gives the source follower an overall gain of almost 1/5 in voltage (-14dB when the ratio of gate voltage to output voltage is expressed in decibels). The benefit of doing this is that the FET has much less work to do. The action of the transformer makes the impedance presented to the FET source bigger by a factor of 42 = 16 times, which is 800 Ohm. The result is improved linearity. Locations differ, but I have never known the active antenna produce unwanted signals. You may be concerned that this low gain would produce a rather 'deaf' receiving system but, from experience, comparing it to a transmitting dipole and tuner, you won't miss much, if anything. The internally-generated noise is very low, and the background noise in most of the HF spectrum is high. 

Power to the active antenna is fed via the coaxial cable, and the supply is injected via choke RFC1 housed in the power-feed unit near the receiver. R4 is included to limit the current in the event of an accidental short-circuit. An LED in series with the supply indicates that current is being drawn, and protects against inadvertent supply polarity reversal.

Shown on the circuit diagram is a power feed for a receiver. This is for the case where the receiver and antenna can share the same power supply. You may choose to omit it. The frequency response is shown in Fig 2, and is nominally flat to within 1dB to 60MHz and within 2dB to 100MHz

CONSTRUCTION 

TRANSFORMER T1 requires some care in construction, and is described in some detail, starting with the quadrifilar wire itself. This would probably be a labourintensive and expensive item to produce commercially, and is where the amateur's craft skills come into their own. Take four strands of 0.2mm diameter (35/36 SWG) enamelled copper wire, length approximately 300mm for each strand. Placing the wires side-by-side, clamp one end and, pulling the wires taut, fix the free end in the chuck of a hand drill. Turn the drill to twist the strands together. There is no need to twist too tightly, a few twists per centimetre being adequate. The core should be a high-permeability (greater than 100) ferrite toroid, 10 to 15mm in diameter. The purpose of the core is to produce a sufficiently high inductance to avoid gain roll-off at low frequencies, and given a high enough permeability, a wide variety of types, still to be found at rallies, should be suitable. If you are buying new, Table 1 shows the types that should be suitable. Supplier contact details are given at the end of the article. Between them, they should be able to source all items needed for construction. Wind seven or eight turns of the quadrifilar wire on the core. (Each time the wire passes through the core counts as one turn.) The photograph shows how this has been done on a T37 -61 core. To secure the winding, the core has been dipped in polyurethane varnish and left to dry. The individual wires need to be separated and the windings identified. Each wire end should be stripped of its insula tion. An easy way to do this is to hold the wire end in a blob of solder on the end of a soldering iron for a few seconds. Make sure you do this in a well-ventilated area and avoid inhaling the fumes or getting them in your eyes. The ends of each winding can then be identified with a multimeter or continuity tester. I found it useful to markthewindings with short strips of insulation stripped from ribbon cable, and slid overthe wires as shown in the same photograph. If you do this with three windings, the fourth can be left plain. Naming the windings arbitrarily 1 to 4, take the end of winding 1, and twist together with the start of winding 2. The end of 2 is then twisted with the start of 3, and so on. Twist fairly close to the toroid, and make electrical connection using the soldering iron, as described above, observing the precautions. The transformer is now complete. Check for electrical continuity through the whole transformer by measuring across the un-paired wires. Once the transformer is done, the rest of the construction is straightforward. Start with R2 as 47 Ohm  or 68 Ohm . It may need to be changed on test. The photograph shows my loft unit built into a diecast box, with a couple of solder tags for earthing to the box. Alternatively, the circuit can be built above a small piece of plain copper-clad board, which can then be fitted inside a weatherproof enclosure if outdoor mounting is required. The enclosure itself can be plastic - it is an antenna after all! Make sure you select the correct tap on transformer T1 for the output, and take care to prevent the unused taps from shorting to any other part of the circuit.

THE POWER FEED 

AS THE PHOTOGRAPH (right) illustrates, I built my power feed unit in a small plastic box. The choke isa single winding of around 20 turns on another high permeability toroid, which can be the same type as that used for the transformer. A metal enclosure would make sense for the power feed unit, since it will be near the receiver and possibly also domestic interference sources. If using a plastic housing, link the coaxial sockets with coaxial cable: I used some RG178. Keep the braid 'tails' short to avoid unwanted pickup.

TESTING AND COMMISSIONING 

CHECK CAREFULLY forwiring errors. For bench testing, the powerfeed and antenna units can be linked with a short coaxial cable. Having ensured that its voltage and polarity are correct, connect the power supply and check that the LED is lit. Measure the voltage across R2 and divide this by its resistance to find the current, or measure the supply current directly. This should be in the region of 10 to 20mA. I selected R2 for a current of around 15mA. Ifthe power feed output is now connected to a receiver, a small amount of additional hiss should be heard. Nothing should be heard until a short wire (1 metre or less) is placed on the antenna input. Signals should be heard on the HF bands, given suitable propagation conditions, or perhaps television or PC monitor timebase harmonics. The antenna unit should be installed as high and as far away from local sources of interference as practicable. Mine is at the apex of the loft, with an antenna wire of around 1 metre length, suspended from a hook in the highest beam. Avoid the temptation to increase the wire length excessively in order to increase the signal. This brings the risk of distortion, and departure  
from a flat gain with frequency. 

POSITIVE - EARTH VERSION 

WITH A NEGATIVE supply and positive earth, a couple of components can be omitted. This is shown in Fig 3, below. However, note that, while this is fine on its own, it must not be connected to a receiver with a negative earth, because this shorts out the supply

=* by Ian Braithwaite, G4COL *= 

Build an Active Antenna

You have heard many times the term “active antenna.” Perhaps you have wondered “exactly what is this antenna and how might it be used?”

Let’s start by defining the word “active.” This does not suggest physical activity on the part of an electronic device. Rather, it tells us that the circuit is active in terms of voltage and current. A passive device, on the other hand, is a circuit that requires no operating voltage. It will exhibit some power loss as a signal is passed through it. Examples of passive devices are diode mixers, filters that use inductance and capacitance (LC filters) and all manner of wire antennas, etc.

An active mixer, on the other hand, uses a transistor or an IC, and operating voltage is applied to it. The mixer draws current and can cause a signal increase from the input to the output terminals. This is known as “conversion gain.” Active antennas contain RF amplifiers that require an operating voltage. Some active circuits may be designed to provide gain, while others may have unity gain (1) or a negative gain (signal loss). The nature of the active circuit depends upon its particular application.
Filters may be made active or passive. An active filter is often used to increase receiver selectivity at audio frequencies. This type of filter has no coils or inductors. Instead, it uses resistors, capacitors and ICs. An active filter may be designed for unity gain, or it may have a gain of 2 or 3, typically.

Active Antennas

What is an active antenna and why might we wish to build one? Active antennas are physically short, and they cover a wide spectrum of frequency. For example, an active antenna may perform uniformly from, say, 550 kHz to 50 MHz if it is designed well. This means that no antenna tuning or matching circuits are needed.
This type of antenna would be quite lossy if it did not include an RF amplifier section. In other words, if you connected a 6-foot whip antenna to your SW receiver and measured a 6.7MHzsignal at S3, that same signal might register 10 dB over S9 on your S meter if you switched to a full size dipole that was cut for 6.7 MHz. However, if we add an RF amplifier to the 6-foot whip before the signal is routed to the receiver, the S meter will indicate a similar reading to that when the dipole is used.

Why Use an Active Antenna?

Active antennas provide an alternative to no antenna at all if you are an apartment dweller or live in an urban area where external antennas are prohibited. These small active antennas are desirable for those who conduct business travel and find it necessary to stay in hotels or motels while on the road. The SWL need not be without an antenna if he is willing to build an active one 

Figure 1: Schematic diagram of the active antenna amplifier. Capacitors without polarity marked are disc ceramic, 50 volts or greater. Resistors are 1/4 watt carbon composition or carbon film. RFC 1 and RFC 2 are miniature iron-core RF chokes (see text). JI and J2 are jacks of the builder's choice. Tl has 12 turns of no. 26 enam. wire (primary winding) on an Amidon Assoc. or FairRite FT-50-43 ferrite toroid core (850 mu). The secondary winding has six turns of no. 26 enam. wire wound uniformly over the primary winding. Overall amplifier gain is approx. 30 dB.

A Simple but Practical Active Antenna

Figure 1 contains a schematic diagram for an active antenna. The parts are inexpensive and easy to obtain. You can tack this circuit together in an evening. It may be constructed on a piece of perf board or a breadboard of your choice. The leads should be kept as short as practicable in order to ensure wide frequency coverage and the prevention of unwanted self-oscillations.
Qt is ajunction field-effect transistor (JFET). It has an input impedance of 1 megohm when wired as shown. This is an ideal situation when we attach a short antenna at JI]. You may use a long telescoping whip antenna, or a short hank of wire may be used. Any length from 6 to 10 feet is okay. Longer pieces of wire may be desirable for reception below 20 MHz. Don’t be afraid to experiment.
Q2 further amplifies the incoming signal (10 dB) and Q3 performs the same function, adding another 10 dB of gain. The gain of Q2 and Q3 may be as great as 15 dB per stage, depending upon the beta of the particular transistor plugged into the circuit. Q2 and Q3 operate as linear broadband amplifiers that use shunt and degenerative feedback. These two stages can be replaced by a single CA3028A or MC1350P IC, should you wish to do your own thing.
The output of Q3 is approximately 200 ohms. A 4:1 broadband step-down transformer (Tl) converts the 200-ohm output to 50 ohms. This makes it suitable for use with most shortwave and amateur receivers.
Although the circuit calls for a 12-V power supply, it will work well at 9V, should you wish to use a battery. Total current drain is on the order of 13 mA at 12 V, and it drops to 8 mA when the supply voltage is lowered to 9.
This circuit works well from 1.6 to 35 MHz. Operation at lower frequencies may be had by changing RCF1 and RFC2 to 10-mH units.

Using the Active Antenna

Connect a short antenna at J]. Vertical polarization will result if the wire or whip is vertical. Moving the antenna to a horizontal position will favor horizontally polarized signals. Be sure to experiment with the orientation of the antenna when monitoring different bands.
In an ideal situation the active antenna and its electronics would be located out of doors (on a balcony, deck or whatever). This will keep it away from electrical house wiring and steel frameworks if you live in an apartment. These man-made objects not only absorb signals but they may radiate noise. You may use RG-58 coaxial cable between the active antenna (T1) and your receiver. Any convenient length is suitable.
If you live near a powerful commercial broadcast station, a CBer with illegal power or an amateur radio station, you may find that the active antenna will overload and cause spurious signals across the tuning range of your receiver. This is a price that must be paid when a broadband circuit is used. Tuned circuits create needed selectivity for eliminating interference from nearby stations with strong signals. Active antennas do not contain tuned circuits.
Build the circuit in a metal box so that it is shielded. You should route the circuit ground to the metal box and ground the box to acold water pipe or an earth ground. This is not an essential action on your part, but it will help to improve the active antenna’s overall performance.
You may substitute 2N4416 FETs for the MPF102 shown at QI of Figure 1. Similarly, you may use 2N4400, 2N4401 or 2N5179 transistors at Q2 and Q3. The 1-mH RF chokes are available from your local store or other store.

=* by Doug Demaw, W1FB *=