Davis W.A.Radio frequency circuit design.2001

230 RF MIXERS

S(t )

1

0

FIGURE 11.6 Single-balanced mixer waveform.

As before, it is assumed that the LO voltage is much greater than the RF voltage, so Vp × V1. The LO voltage can be approximated as a square wave with period T D 1/fp that modulates the incoming RF signal (Fig. 11.6). A Fourier analysis of the square wave results in a switching function designated by S t :

If the input RF signal is expressed as V1 cos 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

f1, fp C f1, 3fp š f1, 5fp š f1, . . .

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

11.5DOUBLE-BALANCED MIXERS

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 two most widely used double balanced mixers for the RF and microwave band are the “ring” mixer and the “star” mixer depicted in Fig. 11.7. 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. The distinguishing feature of the

B

f 0

f 1

(a )

f 0

f p

(b )

FIGURE 11.7 Double-balanced mixers using (a) ring diode design and (b) diode star design.

double-balanced mixer is that half the diodes are on and half off at any given time. The diode pairs are switched on or off according to the local oscillator polarity. Thus the path from the signal port with frequency f1 to the intermediate frequency port, f0, reverses polarity at the rate of 1/fp.

In Fig 11.7a, when the LO is positive at the upper terminal, diodes D1 and D2 are shorted while diodes D3 and D4 are open. Current from the RF port

232 RF MIXERS

flows out of node C. As far as the RF frequency is concerned, nodes A and B lie midway between the positive and negative RF signal voltage. Therefore at the signal frequency, f1, nodes A and B are at zero potential. During this instant, current is drawn from nodes A and B by way of the LO transformer secondary. The RF signal current is induced into the RF transformer secondary and on out to the IF load. When the LO switches to the negative polarity, diodes D3 and D4 are shorted and diodes D1 and D2 are open. The RF signal current will then flow into node D and on to nodes A and B as before. Now, however, the RF current at f1 flows in the opposite direction in the RF signal transformer secondary and thus out of the IF load. The switching of the polarity at the LO frequency, fp, of the current in the IF circuit produces the difference frequency, f0. Symmetry would suggest that the IF power could be extracted from the center tap of the LO secondary rather than the RF signal secondary. However, the LO power, being so much higher than the RF signal power, the isolation between the LO and IF would be poorer.

An analysis of this mixer can be done in SPICE in which the diodes are replaced by ideal voltage switches. An example of this is illustrated in Fig. 11.8 in which the local oscillator is set at 900 MHz and the RF signal is at 800 MHz. The resulting time domain output shown in Fig. 11.9 is not easily interpreted. The Fourier transform in Fig. 11.10 clearly shows the resulting IF output frequency at 100 MHz along with other frequencies generated by the mixer.

The star circuit shown in Fig. 11.7b also acts as a double-balanced mixer. An advantage over the ring mixer is that the central node of the four diodes allows direct connection to the IF circuit. On the other hand, the star mixer requires a more complicated transformer in the RF signal and LO ports. When the LO voltage is positive, diodes D1 and D2 are shorted and diodes D3 and D4 are open. The RF signal current from the upper terminals of the secondary winding flows to the IF port. When the LO voltage is negative, diodes D3 and D4 are shorted and diodes D1 and D2 open. The current then flows from the lower terminals of the RF signal transformer secondary. The RF signal current in the IF circuit has switched polarity. The switching rate produces an output at the difference frequency, f0. In both these cases the switching function is shown in Fig. 11.11. Fourier analysis provides the following time domain representation of the switching function, which differs from Eq. (11.18) by a lack of a dc term:

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

*Ideal voltage switches represent diodes.

* IF output is V(6)

.PRINT TRAN V(6)

.END

FIGURE 11.8 SPICE net list for diode ring mixer.

Clearly, there is no RF signal nor LO voltage seen in the IF circuit, nor any even harmonics of the LO voltage.

The description above of mixers has assumed the use of ideal diodes. The diodes are in fact either pn or Schottky barrier (metal–semiconductor) junctions with a nonzero forward voltage drop and nonzero leakage current in the reverse bias condition. The Schottky barrier devices are particularly useful when low noise is required at high microwave frequencies. The device and package parasitic elements limit mixer frequency response, although designs based on the above analysis have been made to work at frequencies exceeding 26 GHz.

=

FIGURE 11.12 Transmission line transformer equivalent to the center-tapped transformer.

This analysis was also based on the availability of ideal center-tapped transformers. At RF frequencies, these can be realized using transmission line transformers, as shown in Fig. 11.12.

The double-balanced ring mixer described above used a single diode in each arm of the ring. Such a mixer is termed a class 1 mixer. Class 2 mixers are obtained by replacing the single diode in each arm of the ring with two diodes in series or with a diode or resistor in series (Fig. 11.13). The precision resistor in the later case can be adjusted to improve the ring balance and thus the intermodulation distortion. More complex ring elements can be used to further improve intermodulation distortion with the added cost of increasing the amount of LO power required to drive the diodes. More detailed information on design of RF and microwave mixers is available in [3,4].

11.6DOUBLE-BALANCED TRANSISTOR MIXERS

Transistors can also be used as the mixing element in all three types of mixers described above, though only the double-balanced configuration is described here. 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. One example of such a circuit is a transistor ring of enhancement mode n-channel MOSFETs in which the gate voltage must exceed zero in order for the transistor to turn on (Fig. 11.14). When the LO voltage is positive as indicated, the pair of transistors on the right-hand side is turned on, and the

FIGURE 11.13 Double-balanced mixer classes is based on the elements in each branch. Required LO power levels increases with circuit complexity. (From [5].)

left-hand pair is turned off. When the LO voltage is negative, the two pairs of transistors switch roles. In this process the path from the RF signal switches back and forth between the positive and negative IF ports at the LO switching rate. While the balance of the polarity of the RF signal voltage precludes it from being seen at the IF port, the difference frequency generated by the switching action does appear across the IF terminals.

An alternative design is based on the Gilbert cell multiplier [6]. An analysis of the elementary Gilbert cell in Fig. 11.15 is most easily accomplished by assuming that the base and reverse bias saturation currents are negligible, that the output resistances of the transistors are infinite, and that the bias source is ideal. Considering, for the moment, transistors Q1, Q2, and Q5 current continuity demands,

238 RF MIXERS

The ratio of the Schottky diode equations with negligible saturation current gives a second relationship:

Combining of these two equations gives an expression for IC1. In like manner the currents for Q2, Q3, and Q4 are found:

The output voltage is proportional to the difference of the currents through the collector resistors:

D[ IC1 IC4 IC2 IC3 ] R

DR IC5 IC6 R IC5 IC6

1 C e V1/VT 1 C eV1/VT

*Print step, Final time, Print start, Step ceiling

*IF output is V(2,6)

*DC analysis

.TF V(6) VRF *.TF V(6) VP

.END

FIGURE 11.16 SPICE list for the Gilbert multiplier.

Since tanh x ³ x for x − 1, the monomial type of multiplication between the two input voltages will occur as long as Vi − 2VT, where i D 1, 2. At the other extreme, when x × 1, tanh x ³ 1.

The modulator application typically has one large input voltage (LO) and one small one (RF signal). A positive value of the LO voltage, shown as V1 in Fig. 11.15, will then cause Q1 and Q4 to be turned on, while Q2 and Q3 are turned off. As in the previous double-balanced mixers, the LO switches the RF signal voltage path to the IF port at the frequency, fp, so that the difference frequency is generated. A SPICE analysis of the Gilbert cell (Fig. 11.16) again demonstrates the production of an IF output between the collectors of Q1 and Q2.

This same circuit can be realized using field effect transistors. In either case a large RF signal input can cause the mixer to operate outside of its linear region. The mixer dynamic range can be improved by adding emitter (source) degeneracy. This is a small resistor (usually in the 100’s of Ohms) in the emitter circuit. Another scheme is to introduce a filter between the lower two transistors