Wednesday, October 5, 2011

voltage and current sources

Voltage and Current Sources

Real voltage sources can be represented as ideal voltage sources in series with a resistance r, the ideal voltage source having zero resistance. Real current sources can be represented as ideal current sources in parallel with a resistance r, the ideal current source having infinite resistance.

In electric circuit theory, an ideal voltage source is a circuit element where the voltage across it is independent of the current through it. A voltage source is the dual of a current source. In analysis, a voltage source supplies a constant DC or AC potential between its terminals for any current flow through it. Real-world sources of electrical energy, such as batteries, generators, or power systems, can be modeled for analysis purposes as a combination of an ideal voltage source and additional combinations of impedance elements

Working on high voltage power lines, Pearl Harbor

Voltage, otherwise known as electrical potential difference or electric tension (denoted ∆V and measured in volts, or joules per coulomb) is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points. Voltage is equal to the work which would have to be done, per unit charge, against a static electric field to move the charge between two points. A voltage may represent either a source of energy (electromotive force), or it may represent lost or stored energy (potential drop). A voltmeter can be used to measure the voltage (or potential difference) between two points in a system; usually a common reference potential such as the ground of the system is used as one of the points. Voltage can be caused by static electric fields, by electric current through a magnetic field, by time-varying magnetic fields, or a combination of all three.

Voltage is the Cause, Current is the Effect

Voltage attempts to make a current flow, and current will flow if the circuit is complete. Voltage is sometimes described as the 'push' or 'force' of the electricity, it isn't really a force but this may help you to imagine what is happening. It is possible to have voltage without current, but current cannot flow without voltage.


Voltage and Current The switch is closed making a complete circuit so current can flow.	Voltage but No Current The switch is open so the circuit is broken and current cannot flow.	No Voltage and No Current Without the cell there is no source of voltage so current cannot flow.

Voltage, V

Connecting a voltmeter in parallel

Voltage is a measure of the energy carried by the charge.
Strictly: voltage is the "energy per unit charge".
The proper name for voltage is potential difference or p.d. for short, but this term is rarely used in electronics.
Voltage is supplied by the battery (or power supply).
Voltage is used up in components, but not in wires.
We say voltage across a component.
Voltage is measured in volts, V.
Voltage is measured with a voltmeter, connected in parallel.
The symbol V is used for voltage in equations.

Voltage at a point and 0V (zero volts)

Voltage is a difference between two points, but in electronics we often refer to voltage at a point meaning the voltage difference between that point and a reference point of 0V (zero volts). Zero volts could be any point in the circuit, but to be consistent it is normally the negative terminal of the battery or power supply. You will often see circuit diagrams labelled with 0V as a reminder.
You may find it helpful to think of voltage like height in geography. The reference point of zero height is the mean (average) sea level and all heights are measured from that point. The zero volts in an electronic circuit is like the mean sea level in geography.

Zero volts for circuits with a dual supply

Some circuits require a dual supply with three supply connections as shown in the diagram. For these circuits the zero volts reference point is the middle terminal between the two parts of the supply. On complex circuit diagrams using a dual supply the earth symbol is often used to indicate a connection to 0V, this helps to reduce the number of wires drawn on the diagram.
The diagram shows a ±9V dual supply, the positive terminal is +9V, the negative terminal is -9V and the middle terminal is 0V.

Connecting an ammeter in series

Current, I

Current is the rate of flow of charge.
Current is not used up, what flows into a component must flow out.
We say current through a component.
Current is measured in amps (amperes), A.
Current is measured with an ammeter, connected in series.
To connect in series you must break the circuit and put the ammeter acoss the gap, as shown in the diagram.
The symbol I is used for current in equations.
Why is the letter I used for current? ... please see FAQ.

1A (1 amp) is quite a large current for electronics, so mA (milliamps) are often used. m (milli) means "thousandth": 1mA = 0.001A, or 1000mA = 1A
The need to break the circuit to connect in series means that ammeters are difficult to use on soldered circuits. Most testing in electronics is done with voltmeters which can be easily connected without disturbing circuits.

Voltage and Current for components in Series

Voltages add up for components connected in series.
Currents are the same through all components connected in series. In this circuit the 4V across the resistor and the 2V across the LED add up to the battery voltage: 2V + 4V = 6V.
The current through all parts (battery, resistor and LED) is 20mA.

Voltage and Current for components in Parallel

Voltages are the same across all components connected in parallel.
Currents add up for components connected in parallel. In this circuit the battery, resistor and lamp all have 6V across them.
The 30mA current through the resistor and the 60mA current through the lamp add up to the 90mA current through the battery.

RMS value

the root mean square (abbreviated RMS or rms), also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g., sinusoids. RMS is used in various fields, including electrical engineering.
It can be calculated for a series of discrete values or for a continuously varying function. The name comes from the fact that it is the square root of the mean of the squares of the values. It is a special case of the generalized mean with the exponent p = 2.

The RMS value of a set of values (or a continuous-time waveform) is the square root of the arithmetic mean (average) of the squares of the original values (or the square of the function that defines the continuous waveform).
In the case of a set of

n

values $\{x_1,x_2,\dots,x_n\}$ , the RMS value is given by:

$x_{\mathrm{rms}} = \sqrt {{{x_1}^2 + {x_2}^2 + \cdots + {x_n}^2} \over n}.$

The corresponding formula for a continuous function (or waveform)

f (t)

defined over the interval $T_1 \le t \le T_2$ is

$f_{\mathrm{rms}} = \sqrt {{1 \over {T_2-T_1}} {\int_{T_1}^{T_2} {[f(t)]}^2\, dt}},$

and the RMS for a function over all time is

$f_\mathrm{rms} = \lim_{T\rightarrow \infty} \sqrt {{1 \over {2T}} {\int_{-T}^{T} {[f(t)]}^2\, dt}}.$

The RMS over all time of a periodic function is equal to the RMS of one period of the function. The RMS value of a continuous function or signal can be approximated by taking the RMS of a series of equally spaced samples. Additionally, the RMS value of various waveforms can also be determined without calculus, as shown by Cartwright.
In the case of the RMS statistic of a random process, the expected value is used instead of the mean.

RMS of common waveforms

Waveform	Equation	RMS
Sine wave	$y=a\sin(2\pi ft)\,$	$\frac{a}{\sqrt{2}}$
Square wave	$y=\begin{cases}a & \{ft\} < 0.5 \\ -a & \{ft\} > 0.5 \end{cases}$	$a\,$
Modified square wave	$y=\begin{cases}0 & \{ft\} < 0.25 \\ a & 0.25 < \{ft\} < 0.5 \\ 0 & 0.5 < \{ft\} < 0.75 \\ -a & \{ft\} > 0.75 \end{cases}$	$\frac{a}{\sqrt{2}}$
Sawtooth wave	$y=2a\{ft\}-a\,$	$a \over \sqrt 3$
Notes: t is time f is frequency a is amplitude (peak value) {r} is the fractional part of r

Uses

The RMS value of a function is often used in physics and electrical engineering.

Average electrical power

Electrical engineers often need to know the power,

P

, dissipated by an electrical resistance,

R

. It is easy to do the calculation when there is a constant current,

I

, through the resistance. For a load of

R

ohms, power is defined simply as:

$P = I^2 R.\,\!$

However, if the current is a time-varying function,

I (t)

, this formula must be extended to reflect the fact that the current (and thus the instantaneous power) is varying over time. If the function is periodic (such as household AC power), it is nonetheless still meaningful to talk about the average power dissipated over time, which we calculate by taking the simple average of the power at each instant in the waveform or, equivalently, the squared current. That is,

$P_\mathrm{avg}\,\!$	$= \langle I(t)^2R \rangle \,\!$ (where $\langle \ldots \rangle$ denotes the mean of a function)
	$= R\langle I(t)^2 \rangle\,\!$ (as R does not vary over time, it can be factored out)
	$= (I_\mathrm{RMS})^2R\,\!$ (by definition of RMS)

So, the RMS value,

I RMS

, of the function

I (t)

is the constant signal that yields the same power dissipation as the time-averaged power dissipation of the current

I (t)

.
We can also show by the same method that for a time-varying voltage,

V (t)

, with RMS value

V RMS

$P_\mathrm{avg} = {(V_\mathrm{RMS})^2\over R}.\,\!$

This equation can be used for any periodic waveform, such as a sinusoidal or sawtooth waveform, allowing us to calculate the mean power delivered into a specified load.
By taking the square root of both these equations and multiplying them together, we get the equation

$P_\mathrm{avg} = V_\mathrm{RMS}I_\mathrm{RMS}.\,\!$

Both derivations depend on voltage and current being proportional (i.e., the load, R, is purely resistive). Reactive loads (i.e., loads capable of not just dissipating energy but also storing it) are discussed under the topic of AC power.
In the common case of alternating current when

I (t)

is a sinusoidal current, as is approximately true for mains power, the RMS value is easy to calculate from the continuous case equation above. If we define

I p

to be the peak current, then:

$I_{\mathrm{RMS}} = \sqrt {{1 \over {T_2-T_1}} {\int_{T_1}^{T_2} {(I_\mathrm{p}\sin(\omega t)}\, })^2 dt}.\,\!$

where t is time and ω is the angular frequency (ω = 2π/T, whereT is the period of the wave).
Since

I p

is a positive constant:

$I_{\mathrm{RMS}} = I_\mathrm{p}\sqrt {{1 \over {T_2-T_1}} {\int_{T_1}^{T_2} {\sin^2(\omega t)}\, dt}}.$

Using a trigonometric identity to eliminate squaring of trig function:

$I_{\mathrm{RMS}} = I_\mathrm{p}\sqrt {{1 \over {T_2-T_1}} {\int_{T_1}^{T_2} {{1 - \cos(2\omega t) \over 2}}\, dt}}$

$I_{\mathrm{RMS}} = I_\mathrm{p}\sqrt {{1 \over {T_2-T_1}} \left [ {{t \over 2} -{ \sin(2\omega t) \over 4\omega}} \right ]_{T_1}^{T_2} }$

but since the interval is a whole number of complete cycles (per definition of RMS), the

sin

terms will cancel out, leaving:

$I_{\mathrm{RMS}} = I_\mathrm{p}\sqrt {{1 \over {T_2-T_1}} \left [ {{t \over 2}} \right ]_{T_1}^{T_2} } = I_\mathrm{p}\sqrt {{1 \over {T_2-T_1}} {{{T_2-T_1} \over 2}} } = {I_\mathrm{p} \over {\sqrt 2}}.$

A similar analysis leads to the analogous equation for sinusoidal voltage:

$V_{\mathrm{RMS}} = {V_\mathrm{p} \over {\sqrt 2}}.$

Where

I P

represents the peak current and

V P

represents the peak voltage. It bears repeating that these two solutions are for a sinusoidal wave only.
Because of their usefulness in carrying out power calculations, listed voltages for power outlets, e.g. 120 V (USA) or 230 V (Europe), are almost always quoted in RMS values, and not peak values. Peak values can be calculated from RMS values from the above formula, which implies V_p = V_RMS × √2, assuming the source is a pure sine wave. Thus the peak value of the mains voltage in the USA is about 120 × √2, or about 170 volts. The peak-to-peak voltage, being twice this, is about 340 volts. A similar calculation indicates that the peak-to-peak mains voltage in Europe is about 650 volts.
It is also possible to calculate the RMS power of a signal. By analogy with RMS voltage and RMS current, RMS power is the square root of the mean of the square of the power over some specified time period. This quantity, which would be expressed in units of watts (RMS), has no physical significance. However, the term "RMS power" is sometimes used in the audio industry as a synonym for "mean power" or "average power". For a discussion of audio power measurements and their shortcomings, see Audio power.

Amplifier power efficiency

The electrical efficiency of an electronic amplifier is the ratio of mean output power to mean input power. The efficiency of amplifiers is of interest when the energy used is significant, as in high-power amplifiers, or when the power-supply is taken from a battery, as in a transistor-radio.
Efficiency is normally measured under steady-state conditions with a sinusoidal current delivered to a resistive load. The power output is the product of the measured voltage and current (both RMS) delivered to the load. The input power is the power delivered by the DC supply, i.e. the supply voltage multiplied by the supply current. The efficiency is then the output power divided by the input power, and it is always a number less than 1, or, in percentages, less than 100. A good radio frequency power amplifier can achieve an efficiency of 60–80%.
Other definitions of efficiency are possible for time-varying signals. As discussed, if the output is resistive, the mean output power can be found using the RMS values of output current and voltage signals. However, the mean value of the current should be used to calculate the input power. That is, the power delivered by the amplifier supplied by constant voltage

V C C

$P_\mathrm{input}(t) = I_Q V_{CC} + I_\mathrm{out}(t) V_{CC}\,$

where

I Q

is the amplifier's operating current. Clearly, because

V C C

is constant, the time average of

P input

depends on the time average value of

I out

and not its RMS value. That is,

$\langle P_\mathrm{input}(t) \rangle = I_Q V_{CC} + \langle I_\mathrm{out}(t) \rangle V_{CC}.\,$

Root mean square speed

Main article: Root mean square speed

In the physics of gas molecules, the root mean square speed is defined as the square root of the average speed-squared. The RMS speed of an ideal gas is calculated using the following equation:

${v_\mathrm{RMS}} = {\sqrt{3RT \over {M}}}$

where

R

represents the Ideal Gas Constant (in this case, 8.314 J/(mol·K)),

T

is the temperature of the gas in kelvins, and

M

is the molar mass of the gas in kilograms. The generally accepted terminology for speed as compared to velocity is that the former is the scalar magnitude of the latter. Therefore, although the average speed is between zero and the RMS speed, the average velocity for a stationary gas is zero.

Root mean square error

Main article: Root mean square error

When two data sets—one set from theoretical prediction and the other from actual measurement of some physical variable, for instance—are compared, the RMS of the pairwise differences of the two data sets can serve as a measure how far on average the error is from 0.
The mean of the pairwise differences does not measure the variability of the difference, and the variability as indicated by the standard deviation is around the mean instead of 0. Therefore, the RMS of the differences is a meaningful measure of the error.

RMS in frequency domain

The RMS can be computed also in frequency domain. The Parseval's theorem is used. For sampled signal:
$\sum\limits_{n}{{{x}^{2}}(t)}=\frac{\sum\limits_{n}{{{\left| X(f) \right|}^{2}}}}{n}$ , where

X (f) = F F T {x (t)}

n

is number of

x (t)

samples.
In this case, the RMS computed in time domain is the same as in frequency domain:
$RMS=\sqrt{\frac{1}{n}\sum\limits_{n}{{{x}^{2}}(t)}}=\frac{1}{n}\sqrt{\sum\limits_{n}{{{\left| X(f) \right|}^{2}}}}=\sqrt{\sum\limits_{n}{{{\left| \frac{X(f)^{2}}{n} \right|}}}}$

Relationship to the arithmetic mean and the standard deviation

If $\bar{x}$ is the arithmetic mean and

σ x

is the standard deviation of a population or a waveform then:

$x_{\mathrm{rms}}^2 = \bar{x}^2 + \sigma_{x}^2.$

From this it is clear that the RMS value is always greater than or equal to the average, in that the RMS includes the "error" / square deviation as well.
Physical scientists often use the term "root mean square" as a synonym for standard deviation when referring to the square root of the mean squared deviation of a signal from a given baseline or fit.^{[citation needed]} This is useful for electrical engineers in calculating the "AC only" RMS of a signal. Standard deviation being the root mean square of a signal's variation about the mean, rather than about 0, the DC component is removed (i.e. RMS(signal) = Stdev(signal) if the mean signal is 0).

frequency

Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency. The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency. For example, if a newborn baby's heart beats at a frequency of 120 times a minute, its period (the interval between beats) is half a second.

Waveform Conversion, Part I - Sine to Square

The system designer is often called upon to convert a sine wave from an oscillator, power splitter, or other RF device into a square wave suitable for driving a logic device. There are numerous acceptable techniques and the best choice will depend upon several factors including the operating frequency, available signal power, available DC power, acceptable edge speeds, and the characteristics of the logic family.
The simplest technique is to directly couple the sine wave into the logic input with a suitable bias circuit. The sine wave should be a few volts p-p for reliable triggering. This technique is most suitable for CMOS devices in the older 4000 series or HC-MOS and only requires a coupling capacitor and two resistors to bias the input to VCC/2. This simple bias scheme should be avoided with AC-MOS devices unless the frequency and amplitude are high and the input signal is always present. Slow-moving or noisy inputs can cause multiple triggers on any gate, however, and Schmitt trigger inputs are recommended when the input sine wave is large enough to overcome the hysteresis. As an example, the 74HC14 Schmitt trigger has a hysteresis voltage of 0.9 volts so an input sine wave should be a couple of volts at a minimum. The simple biased-gate scheme is shown below:

In some instances the input signal is too small to drive the logic devices but sufficient power is available to drive a step-up transformer or matching circuit. One unusual approach uses a series RLC circuit to step up the voltage. At the input frequency, the RLC network simply looks like a resistor since the inductor and capacitor are series resonant. The resistor value is selected to limit the current at resonance (typically 100 ohms) and the inductive reactance is selected to give the desired gate voltage. In the example below, the inductor is selected to give about 5 volts of swing for the signal input current. It is reasonably safe to use the input protection diodes in AC logic to clamp the swing since AC devices are quite immune to latch-up and the input protection circuit is quite robust.

An ordinary RF step-up transformer may also be used to achieve the higher voltage swing and fairly broadband transformers may be constructed on ordinary ferrite beads, pot cores or miniature balun cores.
Although these techniques will give reasonably reliable results, especially when Schmitt trigger inputs are used, more sophisticated approaches may be desired to handle slow-moving signals or wide signal level variation. The following simple two-transistor differential amplifier will give a good square wave for a wide range of sine wave inputs and it has sufficient gain to square up the edges of slower input frequencies. The differential amplifier approach avoids transistor saturation which often limits the speed of single-transistor circuits. Fast diodes may be used to prevent saturation in single-transistor amplifiers but the cost and complexity usually exceeds the addition of another transistor.

Numerous integrated circuit solutions are also available. Line receivers are an excellent choice and are truly designed for the job. The input stages are typically differential amplifiers offering fairly high input impedance and good speed. Some line receivers have built-in voltage dividers allowing the inputs to handle voltages far beyond the power supply rails and some have built-in voltage references for biasing the input stage. They are also available in combination with line drivers and many have tri-state control inputs. The possible choices are numerous - the line driver, receiver data books are among the thicker volumes on the engineer's bookshelf. Beware that many line receivers have built-in frequency response roll-off making them unsuitable for squaring higher frequency oscillators.
The MC1489 is a typical quad line receiver which operates from a single 5 volt supply and can handle input signals from-30 to +30 volts - but the threshold is internally set. This device features a built-in threshold hysteresis of about 0.3 volts (0.9 for the MC1489A) with the lower threshold near one volt. A "response control" pin is provided to shift the threshold points or to add signal filtering.
Another example is the SN55182 which is a dual differential line receiver that also operates from a single 5 volt supply. It is designed to respond to small differential voltages riding on fairly large common-mode voltages and noise. The inputs may be biased to switch anywhere within the 15 volt bipolar common-mode input voltage range. The input impedance is a few thousand ohms but a built-in 170 ohm line-termination resistor is provided. This line receiver's frequency response may also be lowered by adding an external capacitor and a strobe input is available to force the output to a high level. Since many line receivers operate from a single supply and can sense below ground, the schematic can be quite simple. The following circuit shows 1/2 of the SN55182 connected to convert a sine wave centered around ground - typical of transformer or power splitter outputs. The only external component indicated is a 0.1 uF power supply capacitor! It may be desirable to add an additional resistor to ground at the input to match a particular source or cable impedance.

High-speed comparators may also be used in a similar manner to line receivers but the resistor biasing must be done externally and some amount of hysteresis should be added in the form of a feedback resistor from the output to the positive input to ensure positive switching. Some comparators have "totem pole" outputs which are specifically designed to drive TTL and CMOS loads and some have open-collector outputs which only need a pull-up resistor to achieve suitable logic levels.
Many prescaler devices are specifically designed to handle small sine wave inputs and all that is required is a DC blocking capacitor. The designer should be aware that some prescalers will "free-run" or oscillate when no input signal is present.
High frequency sine waves can often be directly applied to ECL inputs with the appropriate bias circuitry if the sine wave amplitude falls within the ECL's voltage specifications. Some ECL devices have a reference voltage output pin which may be used to bias the input. Simply connect a resistor from the reference to the input and capacitor couple the input signal.

Waveform Conversion, Part II - Square to Sine

Oscillators with logic compatible square wave outputs are not suitable for driving many RF devices since the characteristic impedance is usually well below the desired source impedance and the odd harmonics can generate undesired intermodulation products. Converting a square wave to a sine wave is usually accomplished with either a low pass or bandpass filter and a resistor network to achieve the desired impedance. An amplifier at either the input or output of the filter may be necessary to achieve sufficient signal amplitude.
The circuit below uses a single resistor and a pi network to generate a 50 ohm sine wave from ordinary CMOS logic. The series resistor is selected to limit the current and to isolate the logic device from the reactive load presented by the pi network. The resistor should be a minimum of 200 ohms for most inexpensive clock oscillators and low-power logic devices and the output sine wave level will be about 4 dBm. If the logic device can supply higher current, a 100 ohm resistor may be used to achieve an output level of 10 dBm. AC devices can drive even heavier loads and >13 dBm outputs are practical with a 68 ohm series resistor. The pi network is selected to match the series resistance to 50 ohms at the operating frequency. The Q of the pi network may be low since a square wave has little second harmonic and the third harmonic is three times the fundamental frequency. A low-Q pi network allows the use of fixed values with no adjustments. Add a DC blocking capacitor in series with the output if the load has a DC path to ground. This capacitor may be left out if the load can tolerate DC current and the decreased efficiency is acceptable.

The values for the components of the pi network may be found in many references but for reference the reactances for Q = 2 at three resistances are as follows:
R = 200 ohms, C1 = C2 = 100 ohms reactance, L = 100 ohms reactance
R = 100 ohms, C1 = 50 ohms reactance, C2 = 41 ohms reactance, L = 65 ohms reactance
R = 68 ohms, C1 = 34 ohms reactance, C2 = 30 ohms reactance, L = 50 ohms reactance
The nearest values with these reactances should work well and the actual resistor may be a bit lower since the logic device will have some internal resistance. If a DC blocking capacitor is added in series with the output it should be selected to have a very low reactance at the operating frequency - typically a 0.1 uF.
An ordinary NPN transistor makes an excellent power amplifier for achieving output levels above 13 dBm with light loading of the logic device as shown in the figure below:

The above circuit draws about 12 mA from the 15 volt supply while providing 17 dBm at 6 MHz. The pi network is set to a Q of 4 and a step-down ratio of 4:1. Other output networks are acceptable including tuned transformers or other matching networks. A grounded-gate JFET may be used in place of the NPN transistor eliminating the need for the two base bias resistors and the base bypass capacitor. The U310 is an excellent JFET for frequencies up to several hundred MHz. Reduce the series resistor if the output amplitude is too low - the JFET has a source resistance much higher that the NPN emitter resistance.
A "Tee" network may be used in place of the pi network shown above with some advantages. Since the gate is driving a series inductor instead of a grounded capacitor, the harmonic loading is much less and a series resistor can often be avoided entirely. In applications where the source impedance is not particularly critical and the maximum signal level is desired the Tee network can give excellent results. The circuit below shows an inexpensive clock oscillator driving a tee network to provide about 2 volts p-p into 50 ohms. The network reactances are for Q = 2 and a transformation ratio near 2.5. The reactance values for other network Qs and transformation ratios may be found in RF handbooks and application notes - one favorite is AN-267 from Motorola.

A resistor may be added in series with the gate output as before to achieve a good output VSWR and to protect the gate against shorted outputs. A DC blocking capacitor in series with one of the inductors is recommended for most applications to reduce the loading on the gate and to prevent DC from reaching the load. If a DC blocking capacitor is added it should be selected to have a very low reactance at the operating frequency - typically a 0.1 uF.

Two-Diode Odd-Order Frequency Multipliers

It is often necessary to multiply the frequency of low noise oscillators without significantly degrading the phase noise beyond the theoretical 20 log (N). Low noise frequency doublers constructed with Schottky signal diodes are readily available but higher-order multipliers often exhibit high flicker noise and poor noise floors due to the nature of the switching device. An odd-order diode multiplier topology published in RF Design magazine allows the use of low noise Schottky diodes to generate odd-order harmonics with very low excess noise. A new, half-wave version of the frequency multiplier is presented along with component values for constructing a 10 to 30 MHz tripler and a 10 to 50 MHz quintupler. The conversion loss for these multipliers is good considering their passive design and the input return loss may be easily optimized for different input levels. The circuit for the multiplier is shown below:

The input matching network consists of a choke and capacitor which work together to step up the voltage to overcome the diodes' barrier potential and to provide a low impedance to ground for the desired harmonic while preventing the harmonics form exiting the input. This series tank configuration gives the circuit a degree of feedback which helps to maintain a good conversion loss for a range of input levels. Diode, D1 rectifies the input signal resulting in a DC current in L4. The input signal commutates the two diodes with the result that a square wave of current flows in D2. The output network provides a low impedance to ground for the undesired frequencies and directs the desired harmonic to the output. Other networks may be used in the output circuit but the network should shunt undesired harmonics to preserve the fast diode switching and should block the larger, lower frequency harmonics. (Note: A current meter may be inserted in series with the ground leg of L4 to measure the DC diode current when prototyping.)
This basic configuration may be used for a wide range of frequencies with odd-order multiplication factors to 7 or more. Many fast-switching diode types may be used with excellent results and the choice will depend upon the signal levels and the required phase noise performance. Schottky-barrier diodes such as the 1N5711 are a good choice for most multiplier applications since the conversion efficiency is good and the phase noise performance is better than all but the best sources. Ordinary silicon switching diodes such as the 1N914 will give slightly better conversion efficiency for output frequencies up to 100 MHz but the phase noise performance may be significantly less than provided by Schottky diodes.
Figures 1 and 2 show the conversion loss for a 10 MHz input multiplied to 30 and 50 MHz. The conversion loss is quite low considering the multiplication factor and the 3x multiplier compares favorably with many frequency doublers.

C1 and L1 are selected to give good return loss for the level applied to the input of the multiplier and depends somewhat upon the diode type. Figures 3 and 4 show the return loss for various values of C1 and L1 for the two diode types. For example, if the input level is to be 10dBm, curve #2 would be selected since the return loss is near -30dB. The other component values are selected from the following chart:

C3 may be a 15pF trimmer capacitor for both designs and C2 may be a fixed value with a small trimmer in parallel. The Q of the C2-L2 tank is low and fixed components will usually suffice.

The output of these multipliers may be directly connected to an ordinary MMIC amplifier, if more output is necessary. Choose a low noise figure amplifier if the phase noise performance is critical. The multiplier's intrinsic phase noise can be quite good if constructed with low flicker Schottky diodes. Flicker intercept levels as low as -148 dBc have been realized with the noise floor projected to be near -180 dBc. Few oscillators will be degraded beyond theoretical amounts by such performance.

Tuning Range

Mechanical and/or electrical tuning provisions are provided with most crystal oscillators to adjust the frequency for phase-locking or modulation or to compensate for long-term drift. Mechanical tuning is often accomplished with a single or multi-turn trimmer capacitor or inductor in the crystal circuit which is accessed through a hole in the oscillator housing.
Most Wenzel Associates oscillators employ a varactor diode for all tuning and the mechanical tuning is accomplished internally with a precision potentiometer connected to a precision reference voltage. Our tests have shown that the mechanical stability and hysterisis of the highest quality trimmer potentiometers exceeds the stability of the best precision trimmer capacitors. Electrical tuning is accomplished with the same varactor diode in a configuration yielding high tuning linearity. The mechanical tuning voltage from the potentiometer is applied to the cathode of the tuning diode and the electrical tuning voltage is applied to the anode of the diode through a signal isolating network. The electrical tuning may be centered around zero volts so that in the absence of input the oscillator reverts to the mid-point of the electrical tuning.
As an option, the oscillator's internal reference voltage may be brought out to a pin for connecting to a multi-turn potentiometer for fine tuning. Alternately, a clean DC derived from a separate supply may be applied to the electrical tuning pin. If the available supplies are noisy or unstable, it may be desirable to add a zener diode or reference device and a low-pass noise filter. A temperature compensated zener such as the 1N821 is an excellent choice giving good temperature stability and very low noise - in most instances the 22uF filter capacitor shown below may be left out. Reference devices exhibit excellent stability but they often have rather high noise voltage and the additional filtering is recommended.

Here are a few points to consider:

The amount of tuning range that may be provided is a function of the crystal frequency, cut, overtone, and spot size (or motional capacitance). Precision low frequency oscillators using third-overtone SC-cut crystals will have a tuning range of only a couple of PPM whereas large spot size AT-cut fundamental crystals can achieve over a thousand PPM.
The bandwidth and tuning slope of the electrical tuning input may be specified for PLL applications.
At the time of shipment oven oscillators may exhibit a daily aging rate which would quickly consume all of the mechanical tuning range. This rapid aging will decrase significantly within a few weeks of operation at the oven temperature.
Oven oscillators may use high precision, "stiff" crystals since they operate at a single temperature and the tuning only compensates for aging whereas TCXOs must tune far enough to remove temperature effects as well as compensate for aging.
When an oven oscillator's aging pattern has been established (usually an upward drift) the frequency may be offset in the opposite direction during calibration to nearly double the calibration cycle time.
Linearity is usually specified as a percentage of the total tuning deviation from a straight line fit to the tuning curve. A 10% linearity specification would allow a deviation of 100 Hz away from the best straight line fit for an oscillator with a 1 kHz tuning range. A potential problem is that this deviation can occur rapidly at one end of the range as shown below. The slope is significantly lower at the top of the curve despite the fact that the oscillator meets a fairly tight linearity specification. For PLL systems where the tuning slope impacts the loop stability, it may be appropriate to specify the minimum and maximum tuning slope at all points on the curve in addition to the percent linearity.

Using Precision Oscillators with External References

Many instruments employing precision crystal oscillators as an internal frequency reference have provisions for accepting an external reference as well. The selection of internal or external may be made by manually throwing a switch or it may be automatically triggered by the presence of signal at the external reference input connector. In the simplest of cases the manual switch simply selects which signal source to direct to the instrument and terminates the unused source with an appropriate resistor. When the internal reference is an oven oscillator, it is often desirable to have a "signal-kill" input to turn the oscillator off while leaving the oven operating. TCXOs and non-compensated oscillators may be turned off when the external reference is present to avoid potential interference.
Signal-kill inputs typically accept ordinary TTL levels but they may be configured for custom switching levels without difficulty. Most signal-kill inputs are designed to float to the "on" state when not connected and internal RC circuitry protects the oscillator from damaging voltages or interfering RF signals which might be present on the control line. The circuit shown below will detect the presence of an external reference greater than 1 volt p-p and generate a logic "low" suitable for driving most signal-kill inputs. This control signal could also be used to gate the external input to the instrument's circuitry. The circuit is designed to exhibit a fairly high input impedance so proper cable termination is assumed elsewhere in the instrument.

If the internal oscillator is expected to have better short-term stability than the external reference it may be desirable to phase-lock the internal oscillator to the reference. The locked oscillator will exhibit the good short-term stability of the internal crystal oscillator and the good long-term stability of the external reference. A simple first-order loop may be made with a tri-state bus device or analog switch and a few additional parts. The basic concept is to drive the tri-state control with the external reference signal and pass the internal oscillator signal through one of the tri-stated gates so that the reference signal samples the internal oscillator signal. The output of the tri-state gate is low-pass filtered to remove the RF frequencies and connected to the electrical tuning of the internal oscillator. The tri-state control line is biased such that the gate output "floats" when the external reference is absent. This high-impedance state allows the tuning line to be pulled by a high-value resistor connected to a tuning potentiometer when no external reference is present. The 74HC244 has two sets of four tri-state buffers and is a good choice since the four gates not being used may be employed to buffer the signals.
The following circuit uses the same technique using only two CMOS devices, a 4069 hex inverter and a 4016 or 4066 analog switch. The frequency trimmer potentiometer controls the frequency when no reference is present. The circuit also includes an LED driver to indicate the presence of the external reference signal. Component values are not particularly critical and optimum values will depend upon the application.

The circuit as shown is a first-order loop with most precision oscillators. For example, a 10 MHz oven oscillator might have a tuning sensitivity of 1Hz per volt and, with a 15 volt supply, the phase slope is about 3 volts per radian. The bandwidth of the first-order loop is the product of the tuning sensitivity and the phase slope (1 Hz/volt x 3 volts/rad. = 3 Hz) which is well below the roll-off frequency of the 10k and 10nF network. If the oscillator has a much higher tuning sensitivity, the bandwidth will be proportionally higher and a second-order response may be desired to reduce external reference noise. Although the traditional lossy-integrator op-amp type-2 circuit could be added, additional provisions will be necessary to control the frequency in the absence of the reference since the integrator will tend to wander to one of the supply rails. An alternative way to achieve a second-order response while preserving the automatic tuning switchover is to add an additional passive filter. This type-1 second-order loop is easily achieved by adding a 100k or larger series resistor to the output. Another resistor in series with a capacitor is now added to ground at the output to add an additional roll-off. It may be tempting to simply increase the 10nF capacitor to achieve a lower bandwidth but the damping may become unacceptably low. In fact, if the oscillator has a very wide tuning range, the 10nF may be too large for sufficient damping. (In most reference applications, the first-order loop as shown is usually fine since phase error is not important and the lock bandwidth is not critical.)
Notes:

The circuit above is operating at the frequency limits of the devices at 10 MHz but the 15 volt supply gives about 12 volts of tuning voltage swing without amplification. HCMOS devices will improve the high frequency performance but the lower 5 volt supply will give a smaller tuning voltage range (under 5 volts). An amplifier could be added for oscillators requiring more tuning voltage swing. To calculate the bandwidth of such a system, multiply the amplifier gain by 1.5 to get the amplified phase slope (the 5 volt squarewave will give a 1.5 volt/radian phase slope) and then multiply by the tuning sensitivity of the oscillator.
The reference input may require a resistor to ground on the reference side of the 100nF capacitor to properly terminate the input.
The circuit may be built with tri-state gates but if they are non-inverting gates then a different bias scheme will be required. Remember to bias the external reference gates so that they turn off the tri-state control when no signal is present.
The oscillator tuning input must be a high impedance (megohms). Add a voltage follower to drive lower impedance inputs.

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Wednesday, October 5, 2011