Bài giảng Mạch điện tử thông tin - Chapter 4: RF Mixer (Frequency Converter)

Chapter 4:

RF Mixer

(Frequency Converter)

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Nonlinear Device Characteristics (1)

 A typical mixer is a three-port circuit that accepts two signals at two

different frequencies and produces at the third port a signal that is the sum

or difference of the two input frequencies.

Production of a new frequency or frequencies requires a nonlinear device.

The two most common semiconductor nonlinear characteristics are:

. the form

as found in pn junction diodes or BJTs.

as found in FETs.

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Nonlinear Device Characteristics (2)

 Consider a pn junction nonlinearity that is excited by two signals (plus a

DC term):

The device current is then of the form:

where the thermal voltage, V_T, is defined as kT/q, k is Boltzmann’s

constant, T is the absolute temperature, and q is the magnitude of the

electronic charge.

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Nonlinear Device Characteristics (3)

Using Bessel function:

then

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Nonlinear Device Characteristics (4)

The basic result is a set of frequencies nω_p+ mω₁where n and m can take on

any integer. The usual desired output for a receiver is the intermediate

frequency (IF), ω₀. The frequencies of primary interest are given the

following names:

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Nonlinear Device Characteristics (5)

 In the FET type of nonlinearity, when the mixer is excited by

the output current is

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Figures of Merit for Mixers (1)

The quality of a mixer depends on a number of different mixer parameters

which of course must ﬁt the application under consideration:

 The ﬁrst of these is conversion loss, L. This is the ratio of the delivered

output power to the input available power:

Clearly, the conversion loss is dependent on the load of the input RF circuit as

well as the output impedance of the mixer at the IF port. The conversion loss

for a typical diode mixer is between 6 and 7 dB.

 The noise ﬁgure is a measure of the noise added by the mixer itself to the

RF input signal as it gets converted to the output IF.

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Figures of Merit for Mixers (2)

 The isolation is the amount of local oscillator power that leaks into

either the IF or the RF ports. For double-balanced mixers this value

typically lies in the 15 to 20 dB range.

 The conversion compression is the RF input power, above which the

RF input in terms of the IF output deviates from linearity by a given

amount. For example, the 1-dB compression point occurs when the

conversion loss increases by 1 dB above the conversion loss in the

low-power linear range. A typical value of 1.0 dB compression occurs

when the RF power is +7 dBm and the LO is +13 dBm.

 The LO drive power is the required LO power level needed to make

the mixer operate in optimum. For a double-balanced mixer, this is

typically +6 dBm to +20 dBm.

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Figures of Merit for Mixers (3)

 The dynamic range is the maximum RF input power range for the

mixer. The maximum amplitude is limited by the conversion

compression, and the minimum amplitude is limited by the noise ﬁgure.

The input intercept point is the RF input power at which the output

power levels of the undesired intermodulation products (e.g. IM3) and

the desired IF output would be equal. It conducts to the definition of

spurious free dynamic range (SFDR) (See Chapter 1)

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Single-Ended Mixers

The single-ended mixer in below figure shows that the RF input signal and

the local oscillator signal enter the mixer at the same point. Some degree of

isolation between the two is achieved by using a directional coupler in which

the RF signal enters the direct port and the local oscillator enters through the

coupled port.

The amplitude of the local oscillator is large enough to turn the diode on and

off during each cycle. Indeed, the LO power is so large as to cause clipping

of the LO voltage, thereby approximating a square wave. The small RF

signal is then presented with alternately a short or open circuit at the LO rate.

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Chapter 4:

RF Mixer

(Frequency Converter)

Dept. of Telecomm. Eng.

Faculty of EEE

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1

Single-Balanced Mixers (1)

 The single-balanced (or simply balanced) mixer has either two or four

diodes as shown in four following figures. In all of these cases, when the

LO voltage has a large positive value, all the diodes are shorted. When the

LO voltage has a large negative value, all the diodes are open. In either

case, the LO power cannot reach the IF load nor the RF load because of

circuit symmetry. However, the incoming RF voltage sees alternately a

path to the IF load and a blockage to the IF load. The block may either be

an open circuit to the IF load or a short circuit to ground.

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Single-Balanced Mixers (2)

It is assumed that the LO voltage is much greater than the RF voltage, so

V_p>> V₁. The LO voltage can be approximated as a square wave with

period T = 1/f_pthat modulates the incoming RF signal:

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Single-Balanced Mixers (3)

Fourier analysis of the square wave results in a switching function

designated by S(t):

If the input RF signal is expressed as V₁cos ω₁t, then the output voltage is

this multiplied by the switching function:

Clearly, the RF input signal voltage will be present in the IF circuit.

However, only the odd harmonics of the local oscillator voltage will effect

the IF load. Thus the spurious voltages appearing in the IF circuit are:

and all even harmonics of f_pare suppressed (or balanced out).

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Double-Balanced Mixers (1)

 The double-balanced mixer is capable of isolating both the RF input

voltage and the LO voltage from the IF load. The slight additional cost of

some extra diodes and a balun is usually outweighed by the improved

intermodulation suppression, improved dynamic range, low conversion

loss, and low noise.

The most widely used double balanced mixer for the RF and microwave

band is the “ring” mixer (figure (a)) depicted in below:

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Double-Balanced Mixers (2)

(See pp. 231-232, [2])

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Double-Balanced Mixers (3)

In the single-balanced mixer all the diodes were either turned on or turned off,

depending on the instantaneous polarity of the local oscillator voltage. In the

double-balanced mixer half the diodes are on and half off at any given time,

according to the local oscillator polarity. Thus the path from the RF signal

port with frequency f₁to the IF port, f₀, reverses polarity at the rate of 1/f_p.

In the ring mixer, the switching function is shown as:

Fourier analysis provides the following time domain representation of the

switching function:

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Double-Balanced Mixers (4)

The IF voltage is found as before for the single-balanced mixer:

Clearly, there is no RF signal nor LO voltage seen in the IF circuit, nor

any even harmonics of the LO voltage.

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Double-Balanced Transistor Mixers (1)

 Transistors can also be used as the mixing element in all three types of

mixers described above. These are called active mixers because they

provide the possibility of conversion gain that the diode mixers are not

capable of doing. They produce approximately the same values of port

isolation and suppression of even harmonic distortion as the diode mixers.

Example of single-ended mixer using JFET

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Double-Balanced Transistor Mixers (2)

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Bài giảng Mạch điện tử thông tin - Chapter 4: RF Mixer (Frequency Converter) - Đỗ Hồng Tuấn